
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 that the inequality \[\frac{(x-a)(x-b)}{x-c} \le 0\] is true if and only if either \( x < -6 \) or \( |x-30| \le 2 \). Given that \( a < b \), find the value of \( a + 2b + 3c \).

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