
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 set of unique membership cards. Each card has a sequence of six characters selected from the four letters in MATH and the four digits in 2023. A character may not appear in a sequence more times than it appears in MATH or 2023. Specifically, the digit 2 can appear at most twice, and 3 can appear only once. Find the total number of unique membership card designs, $M$, and compute $\frac{M}{6}$.

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