
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 parabola, given by the equation $y^2 = 2px$ where $p > 0$, has a focus at point $F$. A straight line passing through focus $F$ at an angle of $\frac{\pi}{3}$ intersects the parabola at two points $A$ and $B$. If $|AB| = 8$, find the equation of the parabola.

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