
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:
\[
\begin{pmatrix} 0 & 2c & -2b \\ -2c & 0 & 2a \\ 2b & -2a & 0 \end{pmatrix} 
\begin{pmatrix} 
a^2+d & ab & ac \\ 
ab & b^2+d & bc \\ 
ac & bc & c^2+d 
\end{pmatrix}.
\]
where \(d\) is a real number.

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