
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
Arthur, Bob, and Carla each choose a three-digit number. They each multiply the digits of their own numbers.  Arthur gets 64, Bob gets 35, and Carla gets 81. Then, they add corresponding digits of their numbers together.  The total of the hundreds place is 24, that of the tens place is 12, and that of the ones place is 6. What is the difference between the largest and smallest of the three original numbers?

*Proposed by Jacob Weiner*

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