
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 set of tiles numbered 1 through 36 is modified by a new operation: remove all tiles numbered with either a perfect square or a perfect cube, and then renumber the remaining tiles consecutively starting with 1. Determine the number of times the operation must be performed to reduce the number of tiles in the set to one.

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