
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and they satisfy: $$2 \sqrt {3}a\sin C\sin B=a\sin A+b\sin B-c\sin C$$．
  1. Find the measure of angle $C$;
  2. If $$a\cos( \frac {π}{2}-B)=b\cos(2kπ+A)(k∈Z)$$ and $a=2$, find the area of $\triangle ABC$.

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