
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
The city of Hilltown uses a different format for its bicycle license plates. Each plate consists of four letters: the first chosen from $\{A, E, I, O, U\}$, the second from $\{B, C, D\}$, the third from $\{L, M, N, P\}$, and the fourth from $\{S, T\}$. Hilltown decides to introduce three new letters to increase the number of unique license plates. These new letters can be added to any set, but no more than two letters can be added to a single set. What is the largest possible number of ADDITIONAL license plates that can be made by adding these three letters?

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