
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
Given a right triangle $Rt\triangle ABC$ with $\angle C=90^{\circ}$, solve the triangle under the following conditions:
$(1) \angle B=60^{\circ}, a=4$;
$(2) a= \sqrt {3}-1, b=3- \sqrt {3}$;
$(3) \angle A=60^{\circ}, c=2+ \sqrt {3}$.

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