
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 the function \( f(x) = |x - a| - |x - 4| \) where \( x \in \mathbb{R}, a \in \mathbb{R} \),

(1) If \( a = 2 \), find the range of \( f(x) \);

(2) Under the condition of (1), if there exists an \( x_0 \in \mathbb{R} \) such that \( f(x_0) \leq m - m^2 \), find the range of the real number \( m \).

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