
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
Let point $F$ be the focus of the parabola $y^{2}=2px(p > 0)$. A perpendicular line to the directrix of the parabola is drawn from a point $P$ on the parabola, and the foot of the perpendicular is $Q$. It is known that the line $FQ$ intersects the $y$-axis at point $M(0,2)$ and the area of $\triangle PQF$ is $10$. Find the equation of this parabola.

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