
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
Consider a scenario where motorcycle license plates in Hilltown each contain three sections. The first section is a letter chosen from the set $\{B, F, J, N, T\}$, the second section is a number from $\{1, 2, 3\}$, and the third section is a letter from the set $\{A, E, I, O, U\}$. Hilltown decided to update its license plate format by adding one new letter to the first set and one new number to the second set. What is the largest possible number of ADDITIONAL license plates that can be made with these changes?

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