
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
Petya wants to write out all possible sequences of 100 natural numbers, each of which contains the number three at least once, and where any two adjacent numbers differ by no more than 1. How many sequences will he have to write out?

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