
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 an even function $y=f(x)$ ($x \in \mathbb{R}$), satisfying $f(2-x)=f(x)$, and when $x \in [0, 1]$, $f(x)=x^2$, solve for the number of solutions to the equation $f(x)=\log_{7}|x|$.

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