
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
In the year 2023, a mathematics conference is held in a university where a challenge is presented to the attendees. Let $A$, $B$, and $C$ be distinct positive integers such that the product $A\cdot B\cdot C=3003$. What is the largest possible value of the sum $A+B+C$?

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