
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 $xOy$, with the origin $O$ as the pole and $Ox$ as the polar axis, establish a polar coordinate system. On the curve $C: \rho = 4\sin \theta$, the polar angles corresponding to points $A$ and $B$ are $\frac{π}{6}$ and $\frac{{5π}}{6}$, respectively. Find the area of $\triangle AOB$.

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