
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
In a room, there are 15 chairs arranged in a circle. Three jewelers, when no one is watching, sit on three consecutive chairs, and the jeweler sitting in the middle chair hides a diamond in the chair he is sitting on. The inspector has several detectors that indicate whether or not someone has sat on a chair. What is the minimum number of detectors that need to be placed on the chairs before the jewelers visit, such that their readings can determine where the diamond is hidden?

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