
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
Let $f(x)$ be an even function that satisfies $f(x-1)=f(x+1)$. Given that $f(x)=x$ when $x \in [0,1]$, find the number of solutions to the equation $f(x)={\left( \frac{1}{10}\right)}^{x}$ for $x \in [0,4]$.

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