
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
If two acute angles $\alpha$ and $\beta$ satisfy $(\sin \alpha + \cos \alpha)(\sin \beta + \cos \beta) = 2$, then find the value of $(\sin 2\alpha + \cos 3\beta)^2 + $(\sin 2\beta + \cos 3\alpha)^2$.

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