
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 updated its alphabet soup to include a sixth vowel, Y, along with A, E, I, O, U. Each of the vowels (A, E, I, O, U, and Y) appears five times in the soup (and the consonants do not appear at all). How many six-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