
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 are fewer than 100 cells in a row, and initially, only the cells at both ends contain one piece each. Several classmates take turns placing chess pieces in the cells. Each person places only one piece at a time, and it must be placed in the cell exactly in the middle between two existing pieces (e.g., if pieces are in the 3rd and 7th cells counting from the left, and the 4th, 5th, and 6th cells are empty, a piece can be placed in the 5th cell; but if pieces are in the 4th and 7th cells, and the 5th and 6th cells are empty, then neither the 5th nor the 6th cell can have a piece placed). Each classmate places 9 pieces, ensuring that each cell contains exactly one piece. How many classmates are there in total?

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