
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 continuous even function $f(x)$ on the interval $[-a, a]$ ($a>0$) satisfying $f(0) \cdot f(a) < 0$, and $f(x)$ is a monotonic function on the interval $[0, a]$, determine the number of zeros of the function $y = f(x)$ within the interval $(-a, a)$.

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