
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
Ed now has seven identical green marbles, and a large supply of identical red marbles. He uses some of these red marbles to space between the green ones such that the sequence has equal numbers of marbles whose right hand neighbor is the same color as themselves and whose right hand neighbor is of a different color. Example: GRRGGRGGRRGGRRG. Let $m$ be the maximum number of red marbles Ed can use in one such valid configuration, and let $N$ be the number of ways he can arrange the $m + 7$ marbles to satisfy this requirement. Find the remainder when $N$ is divided by $1000$.

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