
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 such that the number of marbles whose right-hand neighbor is the same color equals the total number of marbles divided by 2. Let $m$ denote the maximum number of blue marbles for which this arrangement is possible. Determine the number of ways Ed can arrange the $m + 7$ marbles to satisfy the requirement and find the remainder when this number is divided by 500.

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