
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 product of the following matrices:
\[
\begin{pmatrix} 0 & d & -b \\ -d & 0 & a \\ b & -a & 0 \end{pmatrix} 
\begin{pmatrix} 2a^2 & ab & ac \\ ab & 2b^2 & bc \\ ac & bc & 2c^2 \end{pmatrix} + 2I,
\]
where \( I \) is the \( 3 \times 3 \) identity matrix, \( a, b, c \) are real numbers, and \( d = a+b \).

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