
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 mathematics club is creating a series of unique keychains. Each keychain contains a sequence of five characters chosen from four letters in STEM and the four digits in 2008. No character may appear in a sequence more times than it appears among the four letters in STEM or the four digits in 2008. A collection of keychains in which each possible sequence appears exactly once contains $M$ keychains. Find $\frac{M}{10}$.

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