
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 $8$ marbles numbered from $1$ to $8.$ Mathew has a bag with $10$ marbles numbered from $1$ to $10.$ I choose three marbles from my bag (where the order of choices does matter) and Mathew chooses one marble from his. How many ways can we choose the marbles such that the sum of the numbers on my three marbles equals the number on Mathew’s marble?

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