
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]


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One hundred carousel seats are arranged in a circle at equal intervals. Each seat is painted in yellow, blue, or red. Seats of the same color are located consecutively and numbered \(1, 2, 3, \ldots\) clockwise. The blue seat No. 7 is opposite to the red seat No. 3, and the yellow seat No. 7 is opposite to the red seat No. 23. Determine the number of yellow seats, blue seats, and red seats on the carousel.

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