
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 $\triangle ABC$, $A=120^{\circ}$, $c > b$, $a= \sqrt {21}$, $S_{\triangle ABC}= \sqrt {3}$, find:
$(1)$ the values of $b$ and $c$.
$(2)$ the value of $\sin B+\cos C$.

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