
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) A traveler stayed at an inn, and the owner agreed to accept rings from the traveler's golden chain as payment for his stay. However, the owner required that the payment be made daily, with one more ring each day than the previous day. The closed chain contained 11 rings, and the traveler planned to stay for exactly 11 days, so he agreed. What is the minimum number of rings the traveler must cut to be able to pay the owner?

b) How many rings should the chain consist of, so that the traveler can stay at the inn for the maximum number of days given that he can cut only $n$ rings?

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