
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 given by
\[ f(x) = \begin{cases} 
x-3 & \text{if } x < 5, \\
\sqrt{x+3} & \text{if } x \ge 5.
\end{cases} \]
The inverse \( f^{-1} \) of this function exists. Calculate \( f^{-1}(-6) + f^{-1}(-5) + \dots + f^{-1}(4) + f^{-1}(5) \).

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