
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
Two polynomials $x^3 + Cx^2 + 15 = 0$ and $x^3 + Dx + 35 = 0$ share a single common root. Find the value of this common root if it is also known that the product of the roots of the first polynomial is $-15$ and of the second polynomial is $-35$.

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