
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 $A$, $B$, $C$ are the three internal angles of $\triangle ABC$, vector $\overrightarrow{m}=(\cos A+1, \sqrt {3})$, $\overrightarrow{n}=(\sin A,1)$, and $\overrightarrow{m}/\!/ \overrightarrow{n}$;
$(1)$ Find angle $A$;  
$(2)$ If $\dfrac {1+\sin 2B}{\cos \;^{2}B-\sin \;^{2}B}=-3$, find $\tan C$.

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