
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 a triangle $\triangle ABC$ with opposite sides $a, b, c$ to angles $A, B, C$ respectively, and it is known that $a^2 - ab - 2b^2 = 0$.
1. If $B = \frac{\pi}{6}$, find the angle $C$.
2. If $C = \frac{2\pi}{3}$ and $c = 14$, find the area $S_{\triangle ABC}$.

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