
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
We call the expression $|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|$ a second-order determinant. Its operation rule is represented by the formula $|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|=ad-bc$. For example, $|\begin{array}{l}{1}&{2}\\{3}&{4}\end{array}|=1\times 4-2\times 3=-2$.  
$(1)$ Please calculate the second-order determinant $|\begin{array}{l}{3}&{-2}\\{4}&{-3}\end{array}|$ according to this rule.  
$(2)$ Simplify the second-order determinant $|\begin{array}{l}{2x-3}&{x+2}\\{2}&{4}\end{array}|$, and find the value of the determinant when $x=4$.

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