
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 ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with left and right foci $F\_1$, $F\_2$, and the point $(1,e)$ and $(e, \frac{\sqrt{21}}{5})$ both on the ellipse, where $e$ is the eccentricity of the ellipse.
(I) Find the equation of the ellipse;
(II) Assume $a > 2$, let $B\_1$, $B\_2$ be the midpoints of the line segments $OF\_1$, $OF\_2$, and draw a line passing through $B\_1$ that intersects the ellipse at points $P$, $Q$. If $PB\_2 \perp QB\_2$, find the area of $\triangle PB\_2Q$.

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