
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 an ellipse with the equation \\( \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)\\) and an eccentricity of \\( \frac{2 \sqrt{2}}{3}\\). Point \\(B(0,1)\\) is a vertex of the ellipse. Line \\(l\\) intersects the ellipse at points \\(P\\) and \\(Q(\neq B)\\) such that \\(BP \perp BQ\\).

1. Find the equation of the ellipse.
2. Find the maximum area of \\(\triangle BPQ\\).

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