
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 quadratic equation in terms of $x$: $x^{2}+\left(2k-1\right)x+k^{2}-k=0$.  
$(1)$ Without solving the equation, determine the situation of the roots of this equation.  
$(2)$ If $x=2$ is one of the roots of the equation, find the value of the algebraic expression $-2k^{2}-6k-5$.

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