
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 the parabola $C$: $y^{2}=2px (p > 0)$ with focus $F$, the point $P$ at which the line $y=4$ intersects $C$, and the point $Q$ at which the line $y=4$ intersects the $y$-axis, such that $|PF|= \frac {3}{2}|PQ|$, find the equation of the parabola $C$ and the coordinates of point $P$.

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