
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
Consider a \(2008 \times 2008\) chess board. Let \(M\) be the smallest number of rectangles that can be drawn on the chess board so that the sides of every cell of the board are contained in the sides of one of the rectangles. Find the value of \(M\).

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