
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
If 2006 integers $a_1, a_2, \ldots a_{2006}$ satisfy the following conditions: $a_1=0$, $|a_2|=|a_1+2|$, $|a_3|=|a_2+2|$, $\ldots$, $|a_{2006}|=|a_{2005}+2|$, then the minimum value of $a_1+a_2+\ldots+a_{2005}$ is.

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