
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
Let $x$ and $y$ be acute angles such that
\begin{align*}
2 \cos^2 x + 3 \cos^2 y &= 1, \\
2 \sin 2x + 3 \sin 2y &= 0.
\end{align*}
Find $2x + y,$ as measured in radians.

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