
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
Let $x_{1}$ and $x_{2}$ be the two real roots of the one-variable quadratic equation $x^{2}-2\left(m+1\right)x+m^{2}+2=0$ with respect to $x$, and $(x_{1}+1)(x_{2}+1)=8$. Find the value of $m$.

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