
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

Find all distinct values of the parameter \( p \) such that the following equation has a unique root. Provide the sum of these values of \( p \) as the answer.

\[ \frac{x^{2}-2 p x+p^{2}+p-20}{x}=0 \]

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