
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 sequence \(\{a_n\}\) has exactly 2003 terms, each of which is a positive integer, and satisfies:
(1) Every term of \(\{a_n\}\) is less than 100;
(2) The sum of any consecutive terms of \(\{a_n\}\) is not equal to 100. Let \(S = \sum_{i=1}^{2003} a_i\). Find the minimum value of \(S\).

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