
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
We attach a square pyramid to two opposite faces of a cube, with the side edges of the two pyramids being equal. Describe the planes of symmetry of the resulting solid, and find all axes that can be used as rotation axes such that rotating the solid by a suitable angle brings it into alignment with itself. Provide a net diagram that can be used to create a paper model for visualization.

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