
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 three internal angles of $\triangle ABC$, and vectors $\overrightarrow{m}=(1, \sqrt {3})$ and $\overrightarrow{n}=(\cos A,\sin A)$ with $\overrightarrow{m} \cdot \overrightarrow{n}=1$.

1. Find angle $A$;
2. If $\frac{1+\sin 2B}{\cos^{2}B-\sin^{2}B}=2$, find $\tan C$.

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