
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
Solve the following equations:

$$
\begin{gathered}
x^{3}-12 x^{2}+47 x-60=0 \\
x^{3}-19 x^{2}+118 x-240=0 \\
x^{4}-18 x^{3}+119 x^{2}-342 x+360=0,
\end{gathered}
$$

Given that in the first equation \( x_{2} + x_{3} = 9 \), in the second equation \( x_{2} x_{3} = 48 \), and in the third equation \( x_{1} + x_{2} = 7 \) and \( x_{3} x_{4} = 30 \).

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