
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 the parabola C: y² = 3x with focus F, and a line l with slope $\frac{3}{2}$ intersecting C at points A and B, and the x-axis at point P.
(1) If |AF| + |BF| = 4, find the equation of line l;
(2) If $\overrightarrow{AP}$ = 3$\overrightarrow{PB}$, find |AB|.

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