
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
If rays are drawn from the center of a cube to its vertices, these rays can be considered as the edges of six tetrahedral angles that divide the entire space. Calculate the magnitudes of the plane angles and dihedral angles of these tetrahedral angles.

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