
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 has seven identical green marbles, and a large supply of identical blue marbles. He arranges the green marbles and some of the blue ones in a row. He finds that the number of marbles whose right-hand neighbor is the same color as themselves is 6 more than the number of marbles whose right-hand neighbor is the other color. An example of such an arrangement is BGBGBGBGBGGBGBB. Let $m$ be the maximum number of blue marbles for which such an arrangement is possible, and let $N$ be the number of ways he can arrange the $m+7$ marbles to satisfy the requirement. Find the value of $N$.

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