
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
A machine produces parts of two types. There are 75 parts laid out in a single line on the conveyor belt. While the conveyor is moving, the machine prepares a part of the type which is less common on the belt. Each minute, the next part falls off the belt, and the prepared part is placed at the end of the belt. After some number of minutes following the start of the conveyor, it may happen that the arrangement of parts on the belt repeats for the first time. Find (a) the smallest such number, and (b) all such numbers.

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