
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 regular hexagonal pyramid, a perpendicular is drawn from the apex to each of its side faces. Connecting the intersection points of these perpendiculars with the base plane forms a hexagon congruent to the base of the pyramid. What are the angles on the side faces of the pyramid?

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