
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
A line passing through the focus of the parabola $y^{2}=2px \left( p > 0 \right)$ intersects the parabola at points $P\left( x_{1},y_{1} \right)$ and $Q\left( x_{2},y_{2} \right)$. If $x_{1}+x_{2}=6$ and $PQ=10$, then the equation of the parabola is __________.

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