
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
Compute the determinant of the following matrix after performing row operations:
\[ 
\text{Let } A = \begin{bmatrix} 3 & 1 & -2 \\ 8 & 5 & -4 \\ 3 & 3 & 7 \end{bmatrix}. 
\]
First subtract the first row from the second and third rows, then compute the determinant of the new matrix.

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