
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 circle with the equation $x^2 + y^2 + 2ax - 2ay + 2a^2 - 4a = 0$ ($0 < a \leq 4$) and its center at $C$, and a line $l: y = x + m$.

(1) If $m = 4$, find the maximum length of the chord intercepted by line $l$ on circle $C$;

(2) If line $l$ is a tangent below the center of the circle, as $a$ varies, find the range of values for $m$.

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