
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
Given $|x_1 - 1| + |x_2 - 2| + |x_3 - 3| + \ldots + |x_{2002} - 2002| + |x_{2003} - 2003| = 0$, find the value of the algebraic expression $2x_1 - 2x_2 - \ldots - 2x_{2002} + 2x_{2003}$.

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