
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
The fourth-degree polynomial \(x^{4}-18 x^{3}+k x^{2}+200 x-1984\) has four roots, and the product of two of these roots is \(-32\). Find the real number \(k\).

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