
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 the fictional language of Zuminton, words consist only of the letters $M, O,$ and $P$. In Zuminton, $O$ is a vowel and both $M$ and $P$ are consonants. A string of these letters forms a valid Zuminton word if and only if between any two $O's$ there are at least three consonants. Determine the number of valid 15-letter Zuminton words, and find the remainder when this number is divided by $1000$.

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