
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
Consider the sequence \( x_{0}, x_{1}, \cdots, x_{2002} \) which satisfies the conditions \( x_{0} = 0 \) and \( \left| x_{n} - x_{n-1} \right| = 1 \) for \( n = 1, 2, \cdots, 2002 \). Find the minimum value of the expression \( x_{1} + x_{2} + \cdots + x_{2002} \).

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