
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 that the slant angle of the straight line $l$ is $60^{\circ}$ and it intersects the parabola $x^2=2py$ ($p > 0$) at points $A$ and $B$. If the sum of the x-coordinates of points $A$ and $B$ is $3$, find the equation of the parabola.

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