
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 \(3 \sin^{2} \alpha + 2 \sin^{2} \beta = 1\) and \(3 (\sin \alpha + \cos \alpha)^{2} - 2 (\sin \beta + \cos \beta)^{2} = 1\), find \(\cos 2 (\alpha + \beta) = \quad \) .

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