
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 \(\alpha\) and \(\beta\) are acute angles, and the following equations hold:
$$
\left\{\begin{array}{l}
3 \sin ^{2} \alpha + 2 \sin ^{2} \beta = 1, \\
3 \sin 2 \alpha - 2 \sin 2 \beta = 0.
\end{array}\right.
$$

Determine \(\alpha + 2\beta\). 

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