
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
Given the function $f(x) = 
\begin{cases} 
x^{2}+1, & \text{for } 0 \leq x \leq 4, \\
2^{x}, & \text{for } -4 \leq x < 0,
\end{cases}$
its inverse function is denoted by $y=f^{-1}(x)$. Find the value of $f^{-1}(4) + f^{-1}\left(\frac{1}{4}\right)$.

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