
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
In the plane rectangular coordinate system \(x O y\), the equation of the ellipse \(C\) is \(\frac{x^{2}}{9}+\frac{y^{2}}{10}=1\). Let \(F\) be the upper focus of \(C\), \(A\) be the right vertex of \(C\), and \(P\) be a moving point on \(C\) located in the first quadrant. Find the maximum area of the quadrilateral \(O A P F\).

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