
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
Ben has four identical blue marbles, and a large supply of identical yellow marbles. He arranges the blue marbles and some of the yellow ones in a row and finds that the number of marbles whose right-hand neighbor is the same color as themselves is equal to the number of marbles whose right-hand neighbor is a different color. An example of such an arrangement could be BYYBYBYBY. Let $m$ be the maximum number of yellow marbles for which such an arrangement is possible, and let $N$ be the number of ways he can arrange the $m+4$ marbles to satisfy the requirement. Find the remainder when $N$ is divided by 1000.

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