
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
Let \( f(x) \) be a function defined on \( \mathbf{R} \) such that \( f(1)=1 \), and for any \( x \in \mathbf{R} \), we have \( f^{\prime}(x)<\frac{1}{2} \). Determine the solution set for the inequality \( f\left(\log _{2} x\right)>\frac{\log _{2} x+1}{2} \).

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