
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
Let the three numbers be x, y, and z. Given that the sum of the three numbers is $36$ and the first number is three times the sum of the other two, then x = 3y + z. Given that the second number is six times the third, then y = 6z. Use this information to calculate the product of the three numbers x, y, and z.

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