
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 matrix product:
\[
\begin{pmatrix} 
0 & d & -e \\ 
-d & 0 & f \\ 
e & -f & 0 
\end{pmatrix} 
\begin{pmatrix} 
x^2 & xy & xz \\ 
xy & y^2 & yz \\ 
xz & yz & z^2 
\end{pmatrix}.
\]

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