
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 $f\left(x\right)$ is an even function defined on $R$, and when $x\leqslant 0$, $f(x)=\log_{\frac{1}{2}}(-x+1)$.  
$(1)$ Find the analytical expression of $f\left(x\right)$;  
$(2)$ If $f\left(a-1\right)-f\left(1\right) \lt 0$, find the range of real number $a$.

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