
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
Given a $2016 \times 2016$ grid, find the smallest positive integer $M$ such that it is possible to draw $M$ rectangles (with sides along the grid lines) where every edge of the small squares in the grid is included in one of the edges of these $M$ rectangles.

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