
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 $a$, $b$, $c$, and $d$ be constants, with $a < b < d$, and suppose that the inequality
\[
\frac{(x-a)(x-b)(x-d)}{x-c} \ge 0
\]
is true if and only if $x \le -7$ or $30 \le x \le 32$. Determine the value of $a + 2b + 3c + 4d$.

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