
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 7 empty boxes on a circle, numbered in a clockwise direction as $1, 2, 3, 4, 5, 6, 7$. Xiao Ming first puts a white piece in box number 1, then puts the second white piece in box number 3, and then puts the third white piece in box number 6, and so on. After placing the $(k-1)$-th white piece, Xiao Ming counts $(k-1)$ boxes in a clockwise direction and places the $k$-th white piece in the next box. Xiao Ming follows this rule to place a total of 200 white pieces. Subsequently, Xiao Qing starts from box number 1 and follows the same rule in a counterclockwise direction to place a total of 300 red pieces in these boxes. Please answer: How many white pieces are there in each box? How many pieces are there in each box?

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