
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
Factorize the following expression:

$$
\begin{gathered}
2(a+b)(b+c)(a+3 b+2 c)+2(b+c)(c+a)(b+3 c+2 a)+ \\
\quad+2(c+a)(a+b)(c+3 a+2 b)+9(a+b)(b+c)(c+a) .
\end{gathered}
$$

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