
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 $y^{2}=2px(p > 0)$ with focus $F$, and a point $M(x_{0},2\sqrt{2})$ on the parabola $C$. A circle centered at $M$ with radius $|MF|$ intersects the $y$-axis, creating a chord of length $2\sqrt{5}$. Find the value of $p$.

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