
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 parabola \( C \) with \( F \) as its focus, and \(|AF| + |BF| = 8\), the perpendicular bisector of segment \( AB \) always passes through a fixed point \( Q(6, 0) \) on the \( x \)-axis.
(1) Find the equation of the parabola \( C \).
(2) Find the maximum area of triangle \( AQB \).

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