
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 an even function f(x) is monotonic on the interval [0, a] where a > 0, and f(0) * f(a) < 0, calculate the number of roots of the equation f(x) = 0 in the interval [-a, a].

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