
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 moving circle C that passes through a fixed point F(2,0) and is tangent to the line x=-2, the locus of the center C of the circle is E.
(1) Find the equation of the locus E.
(2) If a line l intersects E at points P and Q, and the midpoint of the line segment PQ has coordinates (1,1), find the length |PQ|.

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