
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 \(a\), \(b\), and \(c\) be constants, and suppose the inequality \[\frac{(x-a)(x-b)}{x-c} \ge 0\] is true if and only if \(x \le -2\) or \(|x-30| < 2\). Given that \(a < b\), find the value of \(a + 2b + 3c\).

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