
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 *trifecta* is an ordered triple of positive integers  $(a, b, c)$  with  $a < b < c$  such that  $a$  divides  $b$ ,  $b$  divides  $c$ , and  $c$  divides  $ab$ . What is the largest possible sum  $a + b + c$  over all trifectas of three-digit integers?

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