
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 point \( A(2,0) \) and point \( B \) on the elliptical arc
\[ \frac{x^{2}}{4}+\frac{y^{2}}{3}=1 \quad (x > 0, y > 0) \]

Draw a perpendicular from point \( B \) to the y-axis, and let \( C \) be the foot of this perpendicular. What is the maximum value of the area of quadrilateral \( OABC \)?

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