Try round one

.dockerignore

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+.github

.github/workflows/publish-image.yml

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+name: Create and publish Docker runner image
+
+on:
+  workflow_dispatch:
+  schedule:
+    - cron: "0 0 * * *"
+
+env:
+  REGISTRY: ghcr.io
+  IMAGE_NAME: ${{ github.repository }}
+
+jobs:
+  build-and-push0image:
+    runs-on: runner-set-dind
+
+    permissions:
+      packages: write
+      contents: read
+
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v4
+
+      - name: Log in to the Container registry
+        uses: docker/login-action@v3
+        with:
+          registry: ${{ env.REGISTRY }}
+          username: ${{ github.actor }}
+          password: ${{ secrets.GITHUB_TOKEN }}
+
+      - name: Extract metadata (tags, labels) for Docker
+        id: meta
+        uses: docker/metadata-action@v5
+        with:
+          images: ${{ env.REGISTRY }}/${{ env.IMAGE_NAME }}
+
+      - name: Build and push Docker image
+        uses: docker/build-push-action@v5
+        with:
+          context: .
+          push: true
+          tags: ${{ steps.meta.outputs.tags }}
+          labels: ${{ steps.meta.outputs.labels }}

Dockerfile

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+FROM ghcr.io/actions/actions-runner:latest
+
+ARG TARGETOS
+ARG TARGETARCH
+ARG ZIG_VERSION=0.11.0
+ARG CARGO_LAMBDA_VERSION=1.0.3
+
+# Install base packages
+RUN sudo apt update -y \
+    && sudo apt install -y curl wget tar xz-utils unzip build-essential
+
+# Install GH CLI
+RUN curl -fsSL https://cli.github.com/packages/githubcli-archive-keyring.gpg | sudo dd of=/usr/share/keyrings/githubcli-archive-keyring.gpg \
+    && echo "deb [arch=$(dpkg --print-architecture) signed-by=/usr/share/keyrings/githubcli-archive-keyring.gpg] https://cli.github.com/packages stable main" | sudo tee /etc/apt/sources.list.d/github-cli.list > /dev/null \
+    && sudo apt update && sudo apt install -y gh
+
+# Install Rust
+RUN curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh -s -- --default-toolchain stable -y
+ENV PATH="/home/runner/.cargo/bin:${PATH}"
+
+RUN rustup target add aarch64-unknown-linux-musl \
+    && rustup toolchain add nightly
+
+RUN cargo install --locked cargo-lambda@${CARGO_LAMBDA_VERSION}
+
+# Install Zig
+RUN export RUNNER_ARCH=${TARGETARCH} \
+    && if [ "$RUNNER_ARCH" = "arm64" ]; then export RUNNER_ARCH=aarch64 ; fi \
+    && if [ "$RUNNER_ARCH" = "amd64" ]; then export RUNNER_ARCH=x86_64 ; fi \
+    && curl -f -L -o zig.tar.xz https://ziglang.org/download/${ZIG_VERSION}/zig-${TARGETOS}-${RUNNER_ARCH}-${ZIG_VERSION}.tar.xz \
+    && tar xf zig.tar.xz \
+    && rm zig.tar.xz \
+    && mv zig-${TARGETOS}-${RUNNER_ARCH}-${ZIG_VERSION} zig-${ZIG_VERSION}
+
+ENV PATH="/home/runner/zig-${ZIG_VERSION}:${PATH}"
+
+# Install Node v20 and AWS CDK
+RUN curl -fsSL https://deb.nodesource.com/setup_20.x | sudo -E bash - \
+    && sudo apt-get install -y nodejs \
+    && sudo npm i -g aws-cdk
+
+RUN sudo rm -rf /var/lib/apt/lists/*