
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
In Flatville, bicycle license plates contain three letters where the first letter is chosen from the set $\{C, G, L, P, R\}$, the second from $\{A, I, O\}$, and the third from $\{D, M, N, T\}$.
Flatville now adds two new letters to increase the number of unique license plates. The new letters may either go to two different sets or both to the same set. How many ADDITIONAL license plates can be produced if the letters are optimally placed?

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