
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 new language called Zumish, all words consist of the letters $M, O, P,$ and $Z$. Here, $O$ and $Z$ are vowels; $M$ and $P$ are consonants. A string of these letters forms a word in Zumish if and only if between any two vowels, there are at least two consonants. Calculate the number of 12-letter words in Zumish. Determine the remainder when this number is divided by $1000$.

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