
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
Bicycle license plates in Hilltown each contain three letters. The first is chosen from the set $\{B, F, J, M, S\}$, the second from $\{E, U, Y\}$, and the third from $\{G, K, R, Z\}$. Hilltown needed more license plates, so they added two new letters. These new letters were added such that one letter was added to the first set and one to the third set. What is the largest possible 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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