
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 Cyclonia, bicycle license plates also contain three letters. The first letter is chosen from the set $\{B, G, K, Q, W\}$, the second from $\{E, U\}$, and the third from $\{F, J, S, X, Z\}$. 

Cyclonia decided to make more license plates by adding three new letters. These new letters can all be added to one set, or they can be distributed among the sets. Determine 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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