
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 is a grid board of size \(2015 \times 2015\). Dima places detectors in \(k\) cells. Then Kolya places a grid ship in the shape of a square \(1500 \times 1500\) on the board. A detector in a cell informs Dima whether the cell is covered by the ship or not. What is the minimum \(k\) for which Dima can place the detectors so that he can guarantee the ship's position?

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