
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
A complex quartic polynomial \( Q \) is quirky if it has four distinct roots, one of which is the sum of the other three. There are four complex values of \( k \) for which the polynomial \( Q(x) = x^4 - k x^3 - x^2 - x - 45 \) is quirky. Compute the product of these four values of \( k \).

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