
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
In cuboid \( A B C D-A_{1} B_{1} C_{1} D_{1} \), the angle between \( A B_{1} \) and \( A_{1} D \) is \( \alpha \), the angle between \( A C \) and \( B C_{1} \) is \( \beta \), and the angle between \( A_{1} C_{1} \) and \( C D_{1} \) is \( \gamma \). Determine the sum \( \alpha + \beta + \gamma = \qquad \).

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