
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 with dimensions $1 \times 203$. Petya places single-cell detectors on this field, after which Vasya places a two-cell battleship (a rectangle of $1 \times 2$) on it. A detector is triggered if the cell it is placed on is under the battleship. What is the minimum number of detectors Petya should place in order to uniquely determine the position of Vasya's battleship based on their readings?

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