
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 its alphabet soup to include six types of vowels (A, E, I, O, U, Y). In this new version, A appears 3 times, E appears 4 times, I appears 2 times, O appears 5 times, U appears 3 times, and Y appears 3 times. How many five-letter words can be formed from this new bowl of Acme Extended Vowel Soup? (Note: The words do not have to be actual words in English!)

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