
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 parabola is given by the equation y²=2px (p>0). A line l, passing through the focus F of the parabola, intersects the parabola at points A and B. The line l has an inclined angle of π/4. If the distance between the midpoint of AB and the axis of the parabola is 4, find the value of p.

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