
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
Flatville modifies its bicycle license plates which initially contain three letters: the first from $\{B, F, K, S, Z\}$, the second from $\{E, U, Y\}$, and the third from $\{G, J, Q, V\}$. To increase the number of plates, they add two new letters. These new letters can either be both added to one set or one letter can be added to one set and the other to a different set. What is the largest number of additional license plates that can be made by adding these two letters?

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