Nash Equilibrium and Mixed NE Problem

Question

1. Does the game have a pure Nash equilibrium?
2. Find all the mixed equilibria (note, there is at least one)

I'm having some problems solving this exercise about the game between player 1 and 2 in the picture below; from what I understood, checking the best responses of each player to each possible fixed strategy of the other player, there shouldn't be any pure NE in this game. Is this correct? How do I proceed to find the mixed equilibria?

Thank you in advance!