
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 \(O\) is the origin of coordinates, the curve \(C_1: x^2 - y^2 = 1\) intersects the curve \(C_2: y^2 = 2px\) at points \(M\) and \(N\). If the circumcircle of \(\triangle OMN\) passes through the point \(P\left(\frac{7}{2}, 0\right)\), then the equation of the curve \(C_2\) is ____.

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