
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 $F$, and point $A(0, \sqrt{3})$, if point $B$ on parabola $C$ satisfies $AB \perpendicular AF$ and $|BF| = 4$, then $p = \boxed{2 \text{ or } 6}$.

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