diff --git a/go.mod b/go.mod
index bc65238..b85fc12 100644
--- a/go.mod
+++ b/go.mod
@@ -19,7 +19,7 @@ require (
 	github.com/sethvargo/go-envconfig v0.8.0 // indirect
 	github.com/shurcooL/graphql v0.0.0-20220606043923-3cf50f8a0a29 // indirect
 	golang.org/x/crypto v0.0.0-20210817164053-32db794688a5 // indirect
-	golang.org/x/net v0.6.0 // indirect
+	golang.org/x/net v0.7.0 // indirect
 	google.golang.org/appengine v1.6.7 // indirect
 	google.golang.org/protobuf v1.28.0 // indirect
 	gopkg.in/yaml.v3 v3.0.1 // indirect
diff --git a/go.sum b/go.sum
index ea04755..9a060e5 100644
--- a/go.sum
+++ b/go.sum
@@ -35,8 +35,8 @@ golang.org/x/crypto v0.0.0-20210817164053-32db794688a5/go.mod h1:GvvjBRRGRdwPK5y
 golang.org/x/exp v0.0.0-20230213192124-5e25df0256eb h1:PaBZQdo+iSDyHT053FjUCgZQ/9uqVwPOcl7KSWhKn6w=
 golang.org/x/exp v0.0.0-20230213192124-5e25df0256eb/go.mod h1:CxIveKay+FTh1D0yPZemJVgC/95VzuuOLq5Qi4xnoYc=
 golang.org/x/net v0.0.0-20190603091049-60506f45cf65/go.mod h1:HSz+uSET+XFnRR8LxR5pz3Of3rY3CfYBVs4xY44aLks=
-golang.org/x/net v0.6.0 h1:L4ZwwTvKW9gr0ZMS1yrHD9GZhIuVjOBBnaKH+SPQK0Q=
-golang.org/x/net v0.6.0/go.mod h1:2Tu9+aMcznHK/AK1HMvgo6xiTLG5rD5rZLDS+rp2Bjs=
+golang.org/x/net v0.7.0 h1:rJrUqqhjsgNp7KqAIc25s9pZnjU7TUcSY7HcVZjdn1g=
+golang.org/x/net v0.7.0/go.mod h1:2Tu9+aMcznHK/AK1HMvgo6xiTLG5rD5rZLDS+rp2Bjs=
 golang.org/x/oauth2 v0.5.0 h1:HuArIo48skDwlrvM3sEdHXElYslAMsf3KwRkkW4MC4s=
 golang.org/x/oauth2 v0.5.0/go.mod h1:9/XBHVqLaWO3/BRHs5jbpYCnOZVjj5V0ndyaAM7KB4I=
 golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
diff --git a/setup-go/action.yml b/setup-go/action.yml
index af6f5b3..8d56e98 100644
--- a/setup-go/action.yml
+++ b/setup-go/action.yml
@@ -24,14 +24,11 @@ runs:
       uses: actions/cache@v3
       with:
         path: ${{ steps.run.outputs.cache_path }}
-        key: ${{ inputs.cache-key }}-${{ steps.run.outputs.cache_week }}-${{ hashFiles('**/go.mod') }}-${{ hashFiles('**') }}
+        key: ${{ inputs.cache-key }}-${{ steps.run.outputs.cache_week }}-${{ hashFiles('**/go.mod') }}
         restore-keys: |
-          ${{ inputs.cache-key }}-${{ steps.run.outputs.cache_week }}-${{ hashFiles('**/go.mod') }}
-          ${{ inputs.cache-key }}-${{ steps.run.outputs.cache_week }}
+          ${{ inputs.cache-key }}-${{ steps.run.outputs.cache_week }}-
 
     # we don't want them on CI
     - name: Clean test and fuzz caches
-      run: |
-        go clean -testcache
-        go clean -fuzzcache
+      run: go clean -testcache -fuzzcache
       shell: bash
diff --git a/setup-go/main.go b/setup-go/main.go
index da712c7..ccebd1b 100644
--- a/setup-go/main.go
+++ b/setup-go/main.go
@@ -22,6 +22,7 @@ import (
 	"path/filepath"
 	"strconv"
 	"strings"
+	"sync"
 	"time"
 
 	"github.com/sethvargo/go-githubactions"
@@ -29,6 +30,24 @@ import (
 	"github.com/FerretDB/github-actions/internal"
 )
 
+// tidyDir runs `go mod tidy` in the specified directory.
+func tidyDir(action *githubactions.Action, dir string) {
+	cmd := exec.Command("go", "mod", "tidy")
+	cmd.Dir = dir
+	cmd.Stdout = os.Stdout
+	cmd.Stderr = os.Stderr
+
+	start := time.Now()
+
+	action.Infof("Running `%s` in %s ...", strings.Join(cmd.Args, " "), cmd.Dir)
+
+	if err := cmd.Run(); err != nil {
+		action.Fatalf("%s", err)
+	}
+
+	action.Infof("Done in %s.", time.Since(start))
+}
+
 func main() {
 	flag.Parse()
 
@@ -82,6 +101,7 @@ func main() {
 	action.SetOutput("cache_path", gocache)
 
 	// download modules in directories with `go.mod` file
+	var wg sync.WaitGroup
 	err := filepath.Walk(workspace, func(path string, info fs.FileInfo, err error) error {
 		if err != nil {
 			return err
@@ -101,20 +121,17 @@ func main() {
 			return nil
 		}
 
-		cmd := exec.Command("go", "mod", "tidy")
-		cmd.Dir = filepath.Dir(path)
-		cmd.Stdout = os.Stdout
-		cmd.Stderr = os.Stderr
-		start := time.Now()
-		action.Infof("Running `%s` in %s ...", strings.Join(cmd.Args, " "), cmd.Dir)
-		if err = cmd.Run(); err != nil {
-			return err
-		}
-		action.Infof("Done in %s.", time.Since(start))
+		wg.Add(1)
+		go func() {
+			defer wg.Done()
+			tidyDir(action, filepath.Dir(path))
+		}()
 
 		return nil
 	})
 	if err != nil {
 		action.Fatalf("Error walking directory: %s", err)
 	}
+
+	wg.Wait()
 }
diff --git a/tools/go.mod b/tools/go.mod
index 6fe29f3..49aab31 100644
--- a/tools/go.mod
+++ b/tools/go.mod
@@ -201,7 +201,7 @@ require (
 	golang.org/x/exp v0.0.0-20220930202632-ec3f01382ef9 // indirect
 	golang.org/x/exp/typeparams v0.0.0-20220827204233-334a2380cb91 // indirect
 	golang.org/x/mod v0.8.0 // indirect
-	golang.org/x/net v0.6.0 // indirect
+	golang.org/x/net v0.7.0 // indirect
 	golang.org/x/oauth2 v0.0.0-20220411215720-9780585627b5 // indirect
 	golang.org/x/sync v0.1.0 // indirect
 	golang.org/x/sys v0.5.0 // indirect
diff --git a/tools/go.sum b/tools/go.sum
index aae44de..38b0ed9 100644
--- a/tools/go.sum
+++ b/tools/go.sum
@@ -856,8 +856,8 @@ golang.org/x/net v0.0.0-20220412020605-290c469a71a5/go.mod h1:CfG3xpIq0wQ8r1q4Su
 golang.org/x/net v0.0.0-20220425223048-2871e0cb64e4/go.mod h1:CfG3xpIq0wQ8r1q4Su4UZFWDARRcnwPjda9FqA0JpMk=
 golang.org/x/net v0.0.0-20220520000938-2e3eb7b945c2/go.mod h1:CfG3xpIq0wQ8r1q4Su4UZFWDARRcnwPjda9FqA0JpMk=
 golang.org/x/net v0.0.0-20220722155237-a158d28d115b/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c=
-golang.org/x/net v0.6.0 h1:L4ZwwTvKW9gr0ZMS1yrHD9GZhIuVjOBBnaKH+SPQK0Q=
-golang.org/x/net v0.6.0/go.mod h1:2Tu9+aMcznHK/AK1HMvgo6xiTLG5rD5rZLDS+rp2Bjs=
+golang.org/x/net v0.7.0 h1:rJrUqqhjsgNp7KqAIc25s9pZnjU7TUcSY7HcVZjdn1g=
+golang.org/x/net v0.7.0/go.mod h1:2Tu9+aMcznHK/AK1HMvgo6xiTLG5rD5rZLDS+rp2Bjs=
 golang.org/x/oauth2 v0.0.0-20170207211851-4464e7848382/go.mod h1:N/0e6XlmueqKjAGxoOufVs8QHGRruUQn6yWY3a++T0U=
 golang.org/x/oauth2 v0.0.0-20180821212333-d2e6202438be/go.mod h1:N/0e6XlmueqKjAGxoOufVs8QHGRruUQn6yWY3a++T0U=
 golang.org/x/oauth2 v0.0.0-20190226205417-e64efc72b421/go.mod h1:gOpvHmFTYa4IltrdGE7lF6nIHvwfUNPOp7c8zoXwtLw=