
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
Let $M$ be the greatest integer multiple of 8, wherein the last four digits are an arrangement of four distinct digits from 0-9. Furthermore, the last four digits must result from an arithmetic operation $4a - 3b$ where $a$ and $b$ are adjacent pairs of digits in the number. To satisfy this, formulate $M$ such that $a$ and $b$ are digits satisfying the operation, creating a number divisible by 8 but not by 16. What is the remainder when $M$ is divided by 1000?

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