
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
$(Ⅰ)$ Solve the quadratic equation $x^{2}+6x+5=0$; <br/>$(Ⅱ)$ Given a quadratic equation in terms of $x$, $x^{2}-3x+k=0$ has two real roots $x_{1}$ and $x_{2}$. If $(x_{1}-1)(x_{2}-1)=-6$, find the value of $k$ and the solutions of the equation.

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