
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

Using the property that the determinant of a matrix $C = A \cdot B$, which is the product of square matrices $A$ and $B$ of the same order, is equal to the product of the determinants of matrices $A$ and $B$, i.e., $\operatorname{det} C = \operatorname{det} A \cdot \operatorname{det} B$, compute the determinant of matrix $C$.

$$
A = \left(\begin{array}{lll}
3 & 2 & 5 \\
0 & 2 & 8 \\
4 & 1 & 7
\end{array}\right), \quad B = \left(\begin{array}{ccc}
-2 & 3 & 4 \\
-1 & -3 & 5 \\
0 & 4 & 3
\end{array}\right)
$$

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