
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 expanded and now needs even more bicycle license plates. Originally, each plate had three letters where the first was chosen from the set $\{C, H, L, P, R\}$, the second from $\{A, I, O\}$, and the third from $\{D, M, N, T\}$. To accommodate the increase, Flatville decided to add three new letters distributed across these sets. They decided to add one letter to each set. Calculate 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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