
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
Misha has a $100 \times 100$ chessboard and a bag with 199 rooks. In one move, you can either place one rook from the bag on the bottom-left cell, or if there are two rooks on one cell, you can remove one of them and place it on the adjacent cell above or to the right, and return the other to the bag. Misha wants to place 100 rooks on the board so that no two rooks attack each other. Can he achieve any such arrangement?

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