
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 $\triangle ABC$ with opposite sides $a$, $b$, and $c$ corresponding to angles $A$, $B$, and $C$ respectively, and $a^{2}-ab-2b^{2}=0$.

$(1)$ If $B= \frac {\pi}{6}$, find $C$;  
$(2)$ If $C= \frac {2\pi}{3}$ and $c=14$, find the area of $\triangle ABC$.

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