
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]


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Given an even function $f(x)$ that satisfies $f(x-1)=f(x+1)$, and when $x \in [0,1]$, $f(x)=x^{2}$. Find the number of roots of the equation $f(x)=\left( \frac{1}{10} \right)^{|x|}$ in the interval $[-2,3]$.

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