
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
I have a bag with $5$ marbles numbered from $1$ to $5.$ Mathew has a bag with $12$ marbles numbered from $1$ to $12.$ Mathew picks one marble from his bag and I pick two from mine, with the choice order being significant. In how many ways can we choose the marbles such that the sum of the numbers on my marbles exceeds the number on Mathew's marble by exactly one?

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