
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 a polar coordinate system with the origin O as the pole and the positive x-axis as the polar axis, there are two points A(2, $\frac{2}{3}\pi$) and B(3, $\frac{\pi}{6}$). Find the area of triangle $\triangle AOB$.

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