
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 a rectangle, if one of its diagonals forms angles $\alpha$ and $\beta$ with the two sides emanating from one of its vertices, then we have $\cos^2\alpha + \cos^2\beta = \quad$. By analogy, in a rectangular solid, if one of its diagonals forms angles $\alpha$, $\beta$, and $\gamma$ with the three edges emanating from one of its vertices, then the correct equation is $\quad$.

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