
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 series of unique employee IDs. Each ID consists of five characters chosen from the three letters in CAT and the digits in 2021. No character may appear in an ID more times than it appears in CAT or 2021. A set of IDs in which each possible sequence appears exactly once contains $M$ IDs. Calculate $\frac{M}{10}$.

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