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

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