
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 a blackboard. The following operation is performed: each time, erase 3 different numbers and add 2 more of the fourth number that was not erased. For example, if 1 one, 1 two, and 1 three are erased in one operation, write 2 more fours. After performing this operation several times, only 3 numbers remain on the blackboard, and it's no longer possible to perform the operation. What is the product of the remaining three numbers? 


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