
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 that $\sin \theta + \cos \theta = 2 \sin \alpha$ and $\sin 2 \theta = 2 \sin^2 \beta$, find the correct option:
A) $\cos \beta = 2 \cos \alpha$
B) $\cos^2 \beta = 2 \cos^2 \alpha$
C) $\cos 2 \beta = 2 \cos 2 \alpha$
D) $\cos 2 \beta + 2 \cos 2 \alpha = 0$

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