
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 that the values of $a_1, a_2, \ldots, a_{2002}$ are either 1 or -1, let $m$ be the sum of the products of these 2002 numbers taken two at a time.  
(1) Find the maximum and minimum values of $m$, and specify the conditions for achieving these maximum and minimum values;  
(2) Find the minimum positive value of $m$, and specify the conditions for achieving this minimum positive value.

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