Use explicit path to action scripts.

action.yml

@@ -20,18 +20,17 @@ runs:
     - name: Build rustdoc and check it
       shell: bash
       run: |
+        set -euxo pipefail
+
         # Colorize output, since GitHub Actions terminals support color.
         export CARGO_TERM_COLOR=always
 
         # Record the current git sha, so we can come back to it after generating the baseline.
         export CURRENT_GIT_SHA="$(git rev-parse HEAD)"
 
-        # Ensure this action's scripts are available to run on the path.
-        echo "${{ github.action_path }}" >> $GITHUB_PATH
-
         export PACKAGE_NAME="${{ inputs.crate-name }}"
         if [[ "$PACKAGE_NAME" == '' ]]; then
-          export PACKAGE_NAME="$(find_workspace_crates.sh)"
+          export PACKAGE_NAME="$("$GITHUB_ACTION_PATH/find_workspace_crates.sh")"
         fi
         export PACKAGE_NAME_WITH_UNDERSCORES="$(echo $"PACKAGE_NAME" | tr '-' '_')"
 
@@ -41,7 +40,7 @@ runs:
         # We *do not* want to record and reuse the target directory path
         # across different git commits, since it may be at a different location
         # in different commits.
-        git checkout "${{ inputs.version-tag-prefix }}$(find_comparison_version.sh "$PACKAGE_NAME")"
+        git checkout "${{ inputs.version-tag-prefix }}$("$GITHUB_ACTION_PATH/find_comparison_version.sh" "$PACKAGE_NAME")"
         cargo +nightly rustdoc -- -Zunstable-options --output-format json
         mv "$(cargo metadata --format-version 1 | jq -r .target_directory)/doc/$PACKAGE_NAME_WITH_UNDERSCORES.json" /tmp/baseline.json