
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
Sasha wrote no more than one hundred different natural numbers in a circle in random order, and Dima is trying to guess their quantity. To do this, Dima provides Sasha with several positions in a certain order, and then Sasha tells Dima which numbers stand under the specified positions when counting clockwise, starting from the same number. Can Dima always guess the quantity of numbers written by Sasha if he provides:

a) 17 positions;

b) less than 16 positions?

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