
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 a parabola with focus $F$ and equation $y^{2}=2px(p > 0)$, there is a point $A(m,2 \sqrt {2})$ on the parabola. A circle centered at $A$ with radius $|AF|$ intersects the $y$-axis, producing a chord of length $2 \sqrt {7}$. Find the value of $m$.

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