
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
Sasha writes a sequence of natural numbers on the board. The first number \( N > 1 \) is written in advance. He obtains new natural numbers as follows: he either subtracts from or adds to the last written number any of its divisors greater than 1. Will Sasha be able to write the number 2011 on the board at some point for any natural \( N > 1 \)?

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