
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
A rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has  $20$  regular triangular faces,  $30$  square faces, and  $12$  regular pentagonal faces, as shown below. How many rotational symmetries does a rhombicosidodecahedron have?

*2022 CCA Math Bonanza Lightning Round 4.2*

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