
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
On an island, there are knights who always tell the truth and liars who always lie. There are 11 players on the island's football team. Player number 1 said, "There are as many knights as liars on our team." Player number 2 said, "The number of knights and liars on our team differs by one," and so on. Player number 11 said, "The number of knights and liars on our team differs by ten." How many knights are on the team, and if there are any, what are their numbers? Find all possible answers to this question.

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