
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
A company is designing a series of identification tags. Each tag consists of a sequence of five characters taken from the three letters in ABC and the digits in 1228. No character may appear in a sequence more times than it appears in the three letters ABC or the four digits in 1228, and each sequence must contain at least two A's. The complete set of tags where each possible sequence appears exactly once contains $N$ tags. Compute $\frac{N}{10}$.

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