
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
Solve the triangle under the following conditions:  
(1) $b= \sqrt{3}$, $B=60^\circ$, $c=1$;  
(2) $c= \sqrt{6}$, $A=45^\circ$, $a=2$.

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