
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 that for any point M on curve C, the distance from M to point F (1, 0) is 1 less than its distance to the line $l: x = -2$.
(1) Find the equation of curve C;
(2) A line $l$ with a slope of 1 passes through point F and intersects curve C at points A and B. Find the length of segment AB.

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