
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
Consider a \(7 \times 7\) field that is divided into 49 unit squares. Into this field, we want to place tiles in the shape of a Swiss cross, consisting of 5 unit squares. The edges of the crosses should lie on the lines of the field. Determine the smallest possible number of squares that must be marked on the field so that each cross, no matter where it is placed on the field, covers at least one marked square.

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