
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 $A, B, and C$ respectively, and they satisfy $\sin A + \sqrt{3} \cos A = 2$.
(1) Find the measure of angle $A$;
(2) Given three conditions: (1) $a=2$; (2) $B=45^{\circ}$; (3) $c=\sqrt{3}b$. Choose two conditions that can determine triangle $ABC$, and use them to find the area of triangle $ABC$. (Only write one selected combination for scoring; if multiple combinations are written, only the first one will be scored.)

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