
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 satisfies $f(x+2)=f(x)$ for any $x\in[0,+\infty)$. If $f(x)=|x^{2}-x-1|$ when $x\in[0,2)$, find the number of zeros of the function $y=f(x)-1$ on $[-2,4]$.

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