
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 \( a < b < c \) are such that \( b + a \) is divisible by \( b - a \), and \( c + b \) is divisible by \( c - b \). The number \( a \) consists of 2011 digits, and the number \( b \) has 2012 digits. How many digits does the number \( c \) have?

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