
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 similar language, Galaxish, the words consist only of letters $S, T, U$. The letter $U$ is a vowel, and the others are consonants. A string of $S, T, U$ is considered a valid Galaxish word if and only if between any two occurrences of $U$, there must be at least three consonants. Determine the number of 8-letter words in Galaxish that are valid under this rule, and find the remainder when this number is divided by $1000$.

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