
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, where all words consist only of the letters $M, O,$ and $P$, with $O$ as a vowel and $M$ and $P$ as consonants, define a valid word such that no two $O's$ are adjacent without at least two consonants in between. Let $N$ denote the number of 12-letter Zuminglish words. Determine the remainder obtained when $N$ is divided by 2000.

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