
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
Acme Corporation has modified their vowel soup recipe. Now, each of the vowels (A, E, I, O, U) appears in the soup but in different quantities: A appears 8 times, E appears 6 times, I appears 7 times, O appears 5 times, and U appears 4 times. A bowl of this new soup is given. How many five-letter sequences can be formed if a sequence must contain at least one of each vowel at least once?

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