
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
Given the equation \((x-19)(x-83)=p\) has real roots \( r_{1} \) and \( r_{2} \) (where \( p \) is a real number), determine the minimum real root of the equation \(\left(x-r_{1}\right)\left(x-r_{2}\right)=-p\).

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