
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 defined piecewise by
\[ f(x) = \left\{ \begin{aligned} 
2x + 1 & \quad \text{if } x < 1 \\
x^2 & \quad \text{if } x \ge 1 
\end{aligned} \right. \]
Determine the value of \( f^{-1}(-3) + f^{-1}(-1) + f^{-1}(1) + f^{-1}(3) + f^{-1}(9) \).

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