
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
Suppose a city has bicycle license plates with three letters. The first letter is chosen from $\{B, F, J, N, T\}$, the second from $\{E, U\}$, and the third from $\{G, K, R, Z\}$. To increase the number of unique plates, the city decides to add three new letters. One new letter will be added to each set. Determine the largest possible number of ADDITIONAL license plates that can be made.

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