
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
\[
\begin{pmatrix} 0 & d & -e \\ -d & 0 & f \\ e & -f & 0 \end{pmatrix} 
\begin{pmatrix} f^2 & fd & fe \\ fd & d^2 & de \\ fe & de & e^2 \end{pmatrix}.
\]

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