
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
a) Find the sum of the cubes of the roots of the equation \(2x^{2} - 5x + 1 = 0\).

b) Find the value of the expression \(\frac{x_{1}}{x_{2}} + \frac{x_{2}}{x_{1}}\), where \(x_{1}\) and \(x_{2}\) are the roots of the equation \(2x^{2} - 11x + 13 = 0\).

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