
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 internal angles $A$, $B$, and $C$, and vectors $\overrightarrow{m} = (2\cos A, \sin A)$ and $\overrightarrow{n} = (\cos B, -2\sin B)$ such that $\overrightarrow{m} \cdot \overrightarrow{n} = 1$.

1. Find the measure of angle $C$:
2. If the side lengths of $\triangle ABC$ form an arithmetic sequence with a common difference of 4, find the area of $\triangle ABC$.

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