
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
Given the radius of the circumcircle of triangle $\triangle ABC$ is $R$, and $\frac{a^2-c^2}{2R}=(a-b)\sin B$, $\sin B=2\sin A$, $c=2$, determine the area of triangle $\triangle ABC$.

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