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

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