
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
Parabola C is defined by the equation y²=2px (p>0). A line l with slope k passes through point P(-4,0) and intersects with parabola C at points A and B. When k=$\frac{1}{2}$, points A and B coincide.

1. Find the equation of parabola C.
2. If A is the midpoint of PB, find the length of |AB|.

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