
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 $x$, $y$, and $z$ be the three numbers. Given the sum of the three numbers is $20$, express this as an equation. The first number is four times the sum of the other two, express this as an equation. The second number is seven times the third, express this as an equation. Solve the system of equations to find the values of $x$, $y$, and $z$. Then, find the product of all three numbers.

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