
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
The line passing through the focus F of the parabola C: y^{2}=2px (p > 0) intersects the parabola C at points A(x_{1},y_{1}) and B(x_{2},y_{2}). Let |FA|=m and |FB|=n. If n, x_{1}-x_{2}, and m+n form a geometric sequence, find the ratio m/n.

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