
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 that point \( O \) is the origin of coordinates, the curves \( C_{1}: x^{2} - y^{2} = 1 \) and \( C_{2}: y^{2} = 2px \) intersect at points \( M \) and \( N \). If the circumcircle of \( \triangle OMN \) passes through the point \( P\left(\frac{7}{2}, 0\right) \), then what is the equation of the curve \( C_{2} \)?

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