
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  $S(n)$  be the sum of digits for any positive integer n (in decimal notation).
Let  $N=\displaystyle\sum_{k=10^{2003}}^{10{^{2004}-1}} S(k)$ . Determine  $S(N)$ .

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