
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
There are 11 of the number 1, 22 of the number 2, 33 of the number 3, and 44 of the number 4 on the blackboard. The following operation is performed: each time, three different numbers are erased, and the fourth number, which is not erased, is written 2 extra times. For example, if 1 of 1, 1 of 2, and 1 of 3 are erased, then 2 more of 4 are written. After several operations, there are only 3 numbers left on the blackboard, and no further operations can be performed. What is the product of the last three remaining numbers?

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