
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
There's a $2015 \times 2015$ grid board. Dima places detectors in $k$ cells. Then, Kolya places a square-shaped ship of dimensions $1500 \times 1500$ on the board. A detector in a cell reports to Dima whether that cell is covered by the ship or not. What is the minimum $k$ such that Dima can place the detectors in a way that guarantees the reconstruction of the ship's location?

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