
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 the foci of the ellipse $\frac{x^{2}}{4}+y^{2}=1$ are $F\_1$ and $F\_2$, and the parabola $y^{2}=px (p > 0)$ intersects the ellipse at point $Q$ in the first quadrant. If $\angle F\_1QF\_2=60^{\circ}$:

1. Find the area of $\triangle F\_1QF\_2$.
2. Find the equation of the parabola.

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