
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 acute triangle $ABC$, the lengths of the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $b= \sqrt{2}a\sin \;B$.

(1) Find the measure of angle $A$;
(2) If $b= \sqrt{6}$ and $c= \sqrt{3}+1$, find $a.21$ (this might be a typo, I assume it means $a \times 21$).

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