
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 unique ID tags using the letters from the word "MATH" and the digits from the year 2023. Each ID tag is a sequence of five characters where no character appears more times than it appears in "MATH" or "2023". Calculate the total number of unique ID tags possible and find the result divided by 10.

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