
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
Let \( x_{1}, x_{2}, \ldots, x_{n} \) be the roots of the equation \( a_{n} x^{n} + \ldots + a_{1} x + a_{0} = 0 \). What will be the roots of the equations

a) \( a_{0} x^{n} + \ldots + a_{n-1} x + a_{n} = 0 \)

b) \( a_{n} x^{2n} + \ldots + a_{1} x^{2} + a_{0} = 0 \) ?

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