Running headless Codex CLI inside Claude Code

I have both Claude Code CLI and Codex CLI installed on my local machine. I often use Codex to code review or tighten the code on something I am working on. Claude has a better terminal UI, which is not only pleasing to use, but it respects my terminal app's theme. Switching between both CLIs and then finding a way to write prompts wasn't fruitful. So I created a Skill in Claude Code to allow me to…