
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
2023 people will each come into possession of a hat bearing a number between 1 and 2023 (not necessarily distinct). They will only be able to see the numbers on the hats of others and must guess their own without communicating. How can they agree to ensure that at least one person will guess correctly?

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