
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
Arnaldo and Bernardo play a Super Naval Battle. Each has a board  $n \times n$ . Arnaldo puts boats on his board (at least one but not known how many). Each boat occupies the  $n$  houses of a line or a column and the boats they can not overlap or have a common side. Bernardo marks  $m$  houses (representing shots) on your board. After Bernardo marked the houses, Arnaldo says which of them correspond to positions occupied by ships. Bernardo wins, and then discovers the positions of all Arnaldo's boats. Determine the lowest value of  $m$  for which Bernardo can guarantee his victory.

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