
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
Rotate a regular hexagon:
$\alpha$) around one of its diagonals passing through the center,
$\beta$) around one of its midlines.
How do the resulting solids compare in terms of

a) their volumes,

b) their surfaces?

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