
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 that $f(x)$ is an even function defined on $\mathbb{R}$, and for $x \leq 0$, $f(x) = \log_{\frac{1}{2}}(-x+1)$.
1. Find the analytic expression for $f(x)$;
2. If $f(a-1) < -1$, determine the range of real numbers a.

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