
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 $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively, and $(a^{2}+b^{2}-c^{2})\tan C= \sqrt {3}ab$.  
$(1)$ Find angle $C$;  
$(2)$ If $c= \sqrt {7}$ and $b=2$, find the value of side $a$ and the area of $\triangle ABC$.

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