
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 cells of a $2017 \times 100$ board (2017 rows, 100 columns) are colored in a checkerboard pattern. A grasshopper standing on a cell attacks all cells in its row that have the same color as the cell it stands on, and it also attacks all cells in its column that have the opposite color. (To attack a cell, the grasshopper can jump over other pieces.) What is the maximum number of grasshoppers that can be placed on this board without any of them attacking each other?

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