
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 proposition: In a rectangle ABCD on a plane, the angle between the diagonal AC and the sides AB and AD are respectively $\alpha$ and $\beta$, then $\cos^2\alpha + \cos^2\beta = 1$. If we extend it to a spatial cuboid, try to write out the corresponding proposition form.

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