
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
There are 100 thimbles arranged in a circle, with a coin hidden under one of them. In one move, you are allowed to turn over four thimbles and check if the coin is under one of them. After checking, the thimbles are returned to their initial position and the coin moves to a neighboring thimble. What is the minimum number of moves needed to guarantee finding the coin?

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