
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 $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, with $b=c$, and satisfying $\frac{\sin B}{\sin A} = \frac{1-\cos B}{\cos A}$.
1. Find the measure of $\angle A$.
2. If point $O$ is a point outside $\triangle ABC$, with $\angle AOB = \theta$ ($0 < \theta < \pi$), $OA = 2OB = 2$, find the maximum value of the area of the planar quadrilateral $OACB$.

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