
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
For real numbers $a$, $b$, $c$, $d$, a certain operation is defined as $|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|=ad-bc$. For example, $|\begin{array}{l}{1}&{0}\\{2}&{(-2)}\end{array}|=1\times \left(-2\right)-0\times 2=-2$. If $|\begin{array}{l}{(x+1)}&{(x+2)}\\{(x-3)}&{(x-1)}\end{array}|=27$, then $x=\_\_\_\_\_\_$.

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