
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
Place 4 numbers $a$, $b$, $c$, $d$ into 2 rows and 2 columns, and add a vertical line on each side to denote it as $\left|\begin{matrix} a & b \\ c & d \end{matrix}\right|$, and define $\left|\begin{matrix} a & b \\ c & d \end{matrix}\right|=ad-bc$. The notation above is called a 2nd order determinant. If $\left|\begin{matrix} x+1 & 1-x \\ 1-x & x+1 \end{matrix}\right|=8$, then $x=$ ______.

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