
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
Given a set of tiles numbered from 1 to 81, an operation involves alternatingly removing all tiles numbered with a perfect square in the first operation, then all tiles numbered with a prime number in the second operation, and repeating this cycle. The remaining tiles are then renumbered consecutively starting with 1 after each operation. How many operations are needed to reduce the number of tiles in the set to one?
A) 9
B) 10
C) 11
D) 12
E) 13

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