
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 is the smallest non-zero natural number \( n \) that is both the sum of 2010 identical natural numbers, the sum of 2012 identical natural numbers, and the sum of 2013 identical natural numbers?

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