
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
In a language, there are three letters - Ш, У, and Я. A word is defined as a sequence of 100 letters, exactly 40 of which are vowels (У or Я), and the remaining 60 are the letter Ш. What is the maximum number of words that can be chosen so that for any two selected words, there is at least one position among the hundred where different vowels stand simultaneously?

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