
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
A moving circle M passes through a fixed point F(2, 0) and is tangent to the line $x = -2$. The trajectory of the center M of the moving circle is curve C.  
(1) Find the equation of curve C.  
(2) If a line passing through F(2, 0) with a slope of 1 intersects curve C at points A and B, find $|AB|$.

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