
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
Define the function $f(x)$ on $\mathbb{R}$ satisfying $f(1) = 1$, and for any $x \in \mathbb{R}$, $f'(x) < \frac{1}{2}$. Find the solution set for the inequality $f(\log_2 x) > \frac{\log_2 x + 1}{2}$.

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