
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
Arrange the four numbers $a$, $b$, $c$, $d$ into a $2 \times 2$ determinant as $|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|$, which is called a second-order determinant. The operation rule is defined as $|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|=ad-bc$. If $|\begin{array}{l}{x-2}&{x+3}\\{x+1}&{x-2}\end{array}|=13$, then $x=\_\_\_\_\_\_$.

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