
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 Example 1-7, there are 5 characters: $a, b, c, d, e$. Form a string of 6 characters with the following requirements:
1. The 1st and 6th characters must be consonants $b, c, d$.
2. Each string must contain the two vowels $a, e$, and $a$ and $e$ must not be adjacent.
3. Adjacent consonants cannot be the same.

What is the number of such strings?

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