
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
What are the factors of the number 1000000000001? It is easy to answer this question if you know something about numbers of this specific kind. Similarly, it is easy to specify two factors if, instead of 11 zeros, you insert, for example, 101 zeros between the two ones.

There exists an interesting and simple rule for all similar cases. Can you find it?

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