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

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