How should I apply FACT technique on this circuit?

I am learning the fast analytical circuit technique. How could I calculate the pole in the circuit below? I also calculated in the "traditional" way.

I was able to determine the zero and the static gain, but for the pole I would need the time constants that the capacitors "see". If s=0, an open circuit is created.

How should I determine the pole?I also don't understand why if the circuit contains two energy storages, then the transfer function will be first order?

EDIT:If I convert the two capacitors into one capacitor, the pole can be determined. I don't know if this is correct.