
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
Recall that the game "Battleship" starts with placing one "ship" of four cells, two of three cells, three of two cells, and four one-cell ships on a \(10 \times 10\) grid. According to the rules, "ships" should not touch each other, even at the corners. What is the smallest size of a square grid that can be used for this game while maintaining this rule?

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