
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 Zuminglish, a constructed language, all words consist only of the letters $M, O,$ and $P$. In this language, $O$ is considered a vowel while $M$ and $P$ are consonants. A sequence of the letters $M's, O's,$ and $P's$ forms a word in Zuminglish as long as every two occurrences of $O$ are separated by at least two consonants. Define $N$ as the number of 8-letter words in Zuminglish that satisfy these conditions. Determine the remainder when $N$ is divided by $1000$.

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