
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
Assume the vertex of a parabola is at the origin, it opens upward, and point A lies on the parabola. Let F be the focus of the parabola, and M be the intersection of the directrix l and the y-axis. Given that $a=|AM|=\sqrt{17}$ and $|AF|=3$, find the equation of this parabola.

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