
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
Consider the function:
\[ f(x) = \left\{ 
\begin{aligned} 
3x + 1 & \quad \text{ if } x \leq 2 \\
x^2 & \quad \text{ if } x > 2 
\end{aligned} 
\right.\]
The function has an inverse $f^{-1}.$ Find the value of $f^{-1}(-5) + f^{-1}(0) + \dots + f^{-1}(8) + f^{-1}(9)$.

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