Rewrite action/index.js in TypeScript and generate JS using dnt

[magurotuna]

We write plain JavaScript for the entrypoint of GitHub Actions in action/index.js. It becomes bad in terms of developer experience and more prone to easy bugs, as the code gets bigger.
For instance, #319 could have been detected with the type checker if we had written it in TypeScript.

One possible approach to tackle this issue would be to rewrite action/index.js in TypeScript and convert it to Node.js compatible JavaScript using dnt. This way we'd be able to take advantage of type checking during development.