
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
It is easy to place the complete set of ships for the game "Battleship" on a $10 \times 10$ board (see illustration). What is the smallest square board on which this set can be placed? (Recall that according to the rules, ships must not touch each other, even at the corners.)

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