
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 Vowel Soup recipe. Now, the vowels A, E, O appear seven times each in the soup, while I and U still appear five times. How many six-letter "words" can be formed from this new bowl of Acme Vowel Soup, with the condition that the letter I can be used at most twice in any word?

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