
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 measures of the three edges meeting at one vertex of a rectangular prism include one that is the geometric mean of the other two, and the sum of the two smaller measures equals the largest measure. Adding one vertex of the solid to the three neighbors of the opposite vertex, calculate the dihedral angles of the tetrahedron determined by these 4 vertices.

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