
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 a unit right prism \( ABCD-A_1B_1C_1D_1 \), there are two moving points \( E \) and \( F \) on the edges \( BB_1 \) and \( DD_1 \) respectively, such that \( BE = D_1F \). Let the angle between line segment \( EF \) and plane \( AB \) be \(\alpha\), and the angle between line segment \( EF \) and plane \( BC_1 \) be \(\beta\). What is the maximum value of \(\alpha + \beta\)?

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