
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
Given a string of length 5 composed of 26 English letters, find the number of such strings that satisfy the following conditions:
1. The 6 vowels (a, e, i, o, u, y) are not adjacent.
2. No 3 consonants out of the remaining 20 consonants are adjacent.
3. Adjacent consonants are not the same.

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