
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
Let \( T \) be a region in the plane with area 15. When we apply the matrix
\[
\begin{pmatrix} 
3 & 0 \\ 
8 & -2 
\end{pmatrix}
\]
to \( T \), we obtain the region \( T' \). Find the area of \( T' \).

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