
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
The natural numbers from 1 to 2023 are written in a row in some order. It turns out that any three numbers, arranged with one number in between, give different remainders when divided by 3. What number can be in the first place?

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