
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 defined by:
\[ g(x) = \left\{
\begin{array}{cl}
3-x & \text{ if } x \leq 2, \\
3x-x^2 & \text{ if } x > 2.
\end{array}
\right. \]
Calculate \( g^{-1}(-4) + g^{-1}(0) + g^{-1}(5) \).

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