
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 one asymptote of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{3} = 1 (a > 0)$ passes through the point $(2, \sqrt{3})$, and one focus of the hyperbola lies on the axis of the parabola $y^{2} = 2px (p > 0)$, determine the value of $p$.

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