
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
The parabola \\({{x}^{2}}=2py(p > 0)\\) has a focus at \\(F\\), and its directrix intersects with the hyperbola \\(\dfrac{{{x}^{2}}}{3}-\dfrac{{{y}^{2}}}{3}=1\\) at points \\(A,B\\). If \\(\Delta ABF\\) is an equilateral triangle, then \\(P=\\)\_\_\_\_\_\_\_\_\_\_.

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