
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 triangle \(ABC\), the sides \(a\), \(b\), and \(c\) are opposite to angles \(A\), \(B\), and \(C\) respectively, with \(a-2b=0\).
1. If \(B= \dfrac{\pi}{6}\), find \(C\).
2. If \(C= \dfrac{2}{3}\pi\) and \(c=14\), find the area of \(\triangle ABC\).

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