
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 creating a unique series of identification tags. Each tag is designed with a sequence of five characters selected from the four letters in MATH and the four digits in 3119. No character may appear in a sequence more times than it appears in the set of letters MATH or the set of digits 3119. A complete set of tags, containing each valid sequence exactly once, includes $N$ tags. Calculate $\frac{N}{10}$.

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