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

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