
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 integers $x_0, x_1, x_2, x_3, \ldots, x_{2002}, x_{2003}$ satisfying the conditions: $x_0=0$, $|x_1|=|x_0+1|$, $|x_2|=|x_1+1|$, $|x_3|=|x_2+1|$, $\ldots$, $|x_{2003}|=|x_{2002}+1|$,  
find the minimum value of $|x_1+x_2+x_3+\ldots+x_{2002}+x_{2003}|$.

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