
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, the polar coordinates of point A and point B are $(2, \frac{\pi}{3})$ and $(3, 0)$, respectively, with O being the pole. Find:  
(1) $|AB|$;  
(2) The area of $\triangle AOB$.

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