
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 interior angles of triangle ABC, and vectors $$\overrightarrow {m} = (\cos A + 1, \sqrt {3})$$, $$\overrightarrow {n} = (\sin A, 1)$$, and $$\overrightarrow {m}$$ is parallel to $$\overrightarrow {n}$$;  
(1) Find angle A;  
(2) If $$\frac {1+\sin 2B}{\cos^2 B-\sin^2 B} = -3$$, find $\tan C$.

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