
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
Given the sets of letters for the first, second, and third positions of a license plate as $\{C,H,L,P,R\}$, $\{A,I,O\}$, and $\{D,M,N,T\}$, and with the option to add two letters or add one letter to one set and one letter to another set, determine the largest possible number of additional license plates that can be made by adding two letters.

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