
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 a new operation, where the operation rule is $\left|\begin{array}{l}a\;\;\;\;b\\ c\;\;\;\;d\end{array}\right|=ad-bc$. Then $\left|\begin{array}{l}-2\;\;\;\;0.5\\ 2\;\;\;\;\;\;\;\;4\end{array}\right|=\_\_\_\_\_\_$.

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