
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 a function $y=f(x)$ with domain $\mathbb{R}$, for $x > 0$, we have $f(x) > 1$. Also, for any $x$, $y$ in $\mathbb{R}$, $f(x+y) = f(x)f(y)$. Find the solution set of the inequality $f(\log_{\frac{1}{2}}x) \leq \frac{1}{f(\log_{\frac{1}{2}}x + 1)}$.

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