
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
Let \( S(n) \) represent the sum of the digits of the non-negative integer \( n \). For example, \( S(1997) = 1 + 9 + 9 + 7 = 26 \). Find the value of \( S(1) + S(2) + \cdots + S(2012) \).

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