
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
For the smallest value of $n$, the following condition is met: if $n$ crosses are placed in some cells of a $6 \times 6$ table in any order (no more than one cross per cell), three cells will definitely be found forming a strip of length 3 (vertical or horizontal) in each of which a cross is placed.

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