Let $a, b, c$ be real nonzero numbers such that $a + b + c = 12$ and \[ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{abc} = 1. \] Compute the largest possible value of $abc - \left(a + 2b - 3c\right)$.

Let's think step by step and output the final answer within \boxed{}.
user