
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 △ABC, a, b, and c are the sides opposite to angles A, B, and C respectively. Given that 1 + $$\frac{tanC}{tanB}$$ = $$\frac{2a}{b}$$.

1. Find the measure of angle C.
2. If (a+b)<sup>2</sup> - c<sup>2</sup> = 4, find the minimum value of $$\frac{1}{b^{2}}$$ - 3a.

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