Find the thevenin equivalent

This is a tricky one, as the Thevenin resistance of the circuit will be load dependent.

I suggest that you add a 'test' current supply at the output and determine what the input voltage V will be. The Thevenin resistance will be V/I. You'll find that V and V/I depend upon the value of the test current.

If a load resistor R is placed at a-b, then the current through it will V/R. You should be able to use this fact with the expression that you found for the output voltage to find an expression for the power through R.

EDIT: Perhaps I was too hasty in my evaluation. If you just stick a load resistor on the output and solve for the voltage that appears across it, the form of the resulting expression should look very familiar. You should be able to pick the Thevenin voltage and resistance out of it by inspection!