
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 2002 terms, each of which is an integer, and satisfies:
(1) None of the terms \(a_n\) is equal to 119;
(2) The sum of any number of consecutive terms \(|a_n|\) is not equal to 119. Let \(S = a_1 - a_2 + a_3 - \cdots + a_{2002}\). What is the minimum value of \(S\)?

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