
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 club is creating a special batch of membership cards. Each card contains a sequence of six characters chosen from the three letters in CAT and the three digits in 2021. No character may appear in a sequence more times than it appears in the word CAT or the digits in 2021. A complete set of cards, where each possible sequence appears exactly once, contains $M$ membership cards. Calculate $\frac{M}{10}$.

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