
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 ones, 22 twos, 33 threes, and 44 fours on the blackboard. The following operation is performed: each time, three different numbers are erased, and two more of the fourth type of number (the one that was not erased) are added. For instance, if one 1, one 2, and one 3 are erased, then two more of 4 are added. After several operations, only three numbers remain on the blackboard, and no further operations can be performed. What is the product of the remaining three numbers?

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