
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
Suppose \(A\) and \(B\) are two angles such that
\[ \sin A + \sin B = 1 \]
and
\[ \cos A + \cos B = 0. \]

Find the value of \(12 \cos 2A + 4 \cos 2B\).

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