
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
Explain the following facts. The sequence of digits "1221" is considered first as a number in base thirteen, then in base twelve, then in base eleven, and finally in base ten. In each case, we convert our number to the number system with a base that is one less. In the first three cases, the result of the conversion is the same sequence of digits (the same digits in the same order). Why can't the last conversion lead to the same result as the first three cases? - Provide another such sequence of digits.

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