
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 hyperbola $C\_1$: $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$, $(a > 0, b > 0)$ whose focal length is twice the length of the real axis, and the parabola $C\_2$: $x^{2} = 2py$, $(p > 0)$ whose focus is at a distance of 2 from the asymptote of the hyperbola $C\_1$. Find the standard form of the equation of the parabola $C\_2$.

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