
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 Townville, vehicle license plates each contain three letters. The first letter is chosen from the set $\{B, F, J, N, Z\}$, the second letter from $\{E, U, Y\}$, and the third letter from $\{K, Q, X, S\}$. Townville decided to expand their license plate capacity by adding four new letters to these sets. Each new letter could be added to any set, but at least one letter must be added to each of the second and third sets. What is the largest possible number of ADDITIONAL vehicle license plates that can be made by optimally placing these four new letters?

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