
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
The edge angles of a trihedron are equal; let their measure be denoted by $\alpha$. Let the measure of the face angles be $x$. What is the relationship between $\cos \alpha$ and $\cos x$?

What are the values of $\alpha$ and $x$ if they are complementary angles?

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