
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 has decided to modify their bicycle license plates system, which originally contained three letters with the first letter chosen from the set $\{C, H, L, P, R, S\}$, the second from $\{A, E, I, O\}$, and the third from $\{D, M, N, T, V\}$. To accommodate more bicycles, they plan to add three new letters instead of two. These new letters can be added to one set or distributed among the sets. Determine the largest possible number of ADDITIONAL license plates that can be made by adding three letters.

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