
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Let $g$ be a function and $g^{-1}$ be the inverse of $g$. Suppose $g(-1)=2$, $g(0)=3$, and $g(1)=6$, calculate $g^{-1}\left(g^{-1}(6) - g^{-1}(2)\right)$.

Present the answer in LaTex format: \boxed{Your answer}
user