
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
A *trio* is a set of three distinct integers such that two of the numbers are divisors or multiples of the third. Which *trio* contained in  $\{1, 2, ... , 2002\}$  has the largest possible sum? Find all *trios* with the maximum sum.

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