
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
In a group of people who know each other well, each person either always tells the truth or always lies. Sitting around a round table, everyone claims to be a truth-teller but says that the person sitting $k$ seats to their right is a liar. How many people could be sitting around the table?

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