
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
In the equation 
$$
\frac{x^{2}+p}{x}=-\frac{1}{4},
$$
with roots \(x_{1}\) and \(x_{2}\), determine \(p\) such that:

a) \(\frac{x_{1}}{x_{2}}+\frac{x_{2}}{x_{1}}=-\frac{9}{4}\),

b) one root is 1 less than the square of the other root.

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