
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 
\[
\begin{pmatrix} 0 & d & -c \\ -d & 0 & b \\ c & -b & 0 \end{pmatrix} 
\begin{pmatrix} 2a^2 & ab & 2ac \\ ab & 2b^2 & bc \\ 2ac & bc & 2c^2 \end{pmatrix}.
\]

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