
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 y=f(x) such that for \( x \geq 2 \), \( f(x) = (x-2)(a-x) \), where \( a \in \mathbb{R} \), and for \( x \in [0, 2) \), \( f(x) = x(2-x) \).
(1) Determine the expression for f(x) when \( x \leq -2 \);
(2) Discuss under what conditions for real numbers \( a \) and \( m \), the function \( g(x) = f(x) - m \) has four zeros, which form an arithmetic sequence from smallest to largest.

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