
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
Flatville is expanding its system for generating bicycle license plates, originally containing three letters where the first letter is chosen from the set {C, H, L, P, R}, the second from {A, I, O}, and the third from {D, M, N, T}. To generate more license plates, Flatville decides to add one new letter to both the first and the second set of letters. Determine the largest possible number of ADDITIONAL license plates that can be made if the choices for the first set increase to six and the choices for the second set increase to four, while keeping the third set unchanged.

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