
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 CycleCity, bicycle license plates each contain three letters. The first letter is chosen from the set $\{B, F, J, M, Q\}$, the second from $\{E, U\}$, and the third from $\{K, S, V, Y\}$. CycleCity decided to increase the number of available license plates by adding two new letters. These new letters can either be added to one letter set or split between two sets. What is the largest possible number of ADDITIONAL license plates that can be produced by adding these two letters?

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