
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 a function $y = f(x)$ defined on $\mathbb{R}$ that is an even function satisfying $f(2 + x) = f(2 - x)$. If the function $y = f(x)$ has at least one zero in the interval $(0, 4)$ and $f(0) = 0$, then determine the number of zeros of the function $y = f(x)$ in the interval $(-8, 10]$.

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