
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 $p,$ $q,$ and $r$ be constants, and suppose that the inequality \[\frac{(x-p)(x-q)}{x-r} \geq 0\] is true if and only if either $x < -6$ or $|x-20| \le 2.$ Given that $p < q,$ find the value of $p + 2q + 3r.$

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