
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
The equations $x^3 + 2Ax + 20 = 0$ and $x^3 + 3Bx^2 + 100 = 0$ have two roots in common. Find the product of these common roots in the simplest form, expressed as $k \sqrt[d]{m}$, where $k$, $d$, and $m$ are positive integers when simplified. Determine $k + d + m$.

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