
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 line passing through the focus \(F\) of the parabola \(y^{2}=2px\ (p > 0)\) forms a \(45^{\circ}\) angle with the horizontal axis and intersects the parabola at points \(A\) and \(B\). If the length of segment \(AB\) is \(8\), find the value of \(p\).

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