
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
Given a parabola $y = x^2 - (k-1)x - 3k - 2$ intersects the x-axis at points $A (\alpha, 0)$ and $B (\beta, 0)$, and $\alpha^2 + \beta^2 = 17$, then $k = \quad$.

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