
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 that $A$, $B$, and $C$ are the internal angles of $\triangle ABC$, and $\tan A$ and $\tan B$ are the two real roots of the equation $x^{2}+ \sqrt {3}mx-m+1=0$ with respect to $x$.

1. Find the size of $C$.
2. If $AB= \sqrt {6}$ and $AC=2$, find the area $S$ of $\triangle ABC$.

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