
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
The playing field for the game "Battleship" is a rectangle $1 \times 203$. Petya places single-cell detectors on this field, after which Vasya places a two-deck ship (a rectangle $1 \times 2$). A detector is triggered if the cell on which it is placed is under the ship. What is the minimum number of detectors Petya must place to uniquely determine the position of Vasya's ship?

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