
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 $f(x)= \begin{cases} 3^{x+1}, & x\leqslant 0 \\ \log_{\frac{1}{2}}x, & x > 0\end{cases}$, find the solution set for the inequality $f(x) > 1$.

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