
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 $\triangle ABC$, $a$, $b$, $c$ are the opposite sides of angles $A$, $B$, $C$ respectively, and $asinC=ccos(A-\frac{π}{6})$.  
$(1)$ Find $A$;  
$(2)$ Given $a=\sqrt{7}$, ____, calculate the area of $\triangle ABC$.  
Choose one of the conditions from $b=2$ and $3\sin C=2\sin B$ to complete and answer question (2). (Note: If multiple conditions are chosen to answer separately, points will be awarded based on the first answer.)

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