Universal Login And Signup form

This design aims to combine both Login and Signup forms into one.

On various apps, I've mistakenly entered my email address and password to login, only realising later it was for the signup section. Then I have to switch to login and retype my details. Frustrating!

I think the server logic should be:
- Push users towards o-auth services like facebook/google
- Check if an account exists already, if it does, log them in
- If no previous records exist, assume they are a new user and direct them to the onboarding process.

Potential problems:
- User mistypes their email address and a new account is created. Existing user doesn't know where their previous account data is.
- Extra verbiage: "Login or Signup" required
- Most users are used to two forms for different actions.

Benefits:
- Single form for both login and signup. One less click.
- Clean and less elements (no extra tabs).

Thoughts?