
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
Do the following equations have common roots?

\[
\begin{aligned}
& 3x^{4} + 13x^{3} + 20x^{2} + 17x + 7 = 0 \\
& 3x^{4} + x^{3} - 8x^{2} + 11x - 7 = 0
\end{aligned}
\]

Solve both equations.

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