
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 line $l$ passing through the focus $F$ of the parabola $y^{2}=2px(p > 0)$ intersects the parabola in the first quadrant at point $A$ and intersects the directrix of the parabola at point $B$. The projection of point $A$ on the directrix of the parabola is point $C$. If $\overrightarrow{AF}= \overrightarrow{FB}$ and $\overrightarrow{BA} \cdot \overrightarrow{BC}=48$, then the equation of the parabola is \_\_\_\_\_\_.

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