
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
Define an operation: $|\begin{array}{l}{a}&{c}\\{b}&{d}\end{array}|=ad-bc$. For example, if $|\begin{array}{l}{1}&{3}\\{-2}&{0}\end{array}|=1\times 0-\left(-2\right)\times 3=6$, then when $a=-1^{2}$, $b=\left(-2\right)^{2}-1$, $c=-3^{2}+5$, $d=\frac{3}{4}÷(-\frac{1}{4})$, find the value of $|\begin{array}{l}{a}&{c}\\{b}&{d}\end{array}|$.

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