
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 town of Gearville, each bike license plate consists of three letters. The first letter is chosen from the set $\{B, F, G, T, Y\}$, the second from $\{E, U\}$, and the third from $\{K, S, W\}$. Gearville decided to increase the number of possible license plates by adding three new letters. These new letters can be added to one set or distributed among the sets. What is the largest possible number of ADDITIONAL license plates that can be created by optimally placing these three letters?

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