
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 polar coordinate system with the origin \\(O\\) as the pole and the positive half of the \\(x\\)-axis as the polar axis, given two points \\(A(2,\dfrac{2}{3}\pi), B(3,\dfrac{\pi}{6})\\), the area of \\(\triangle AOB\\) is \_\_\_\_\_\_.

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