
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 cross pattern consisting of five cells (one cell and all its neighbors) is placed on a $5 \times 5$ board. What is the minimum number of detectors that must be placed on the board in order to determine the exact position of the cross? (A detector indicates whether the cell belongs to the cross or not, and all detectors operate simultaneously.)

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