
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 upgraded their alphabet soup to include the vowels A, E, I, O, U, and Y, each appearing five times in the soup, except for A, which appears only three times. How many five-letter words can be formed under these constraints, where the words do not have to be actual words in English?

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