
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 \(C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) and a line \(l\) that intersects the ellipse \(C\) at points \(P\) and \(Q\) without being perpendicular to the \(x\)-axis, point \(S\) is the reflection of point \(P\) about the \(x\)-axis. Find the maximum area of the triangle \(\triangle OSQ\).

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