
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
(Full score of this question is 12 points) Arrange all the extreme points of the function $f(x) = \sin x \cdot \sin(x + 2\pi) \cdot \sin(x + 3\pi)$ in the interval $(0, +\infty)$ in ascending order to form a sequence $\{a_n\} (n \in \mathbb{N}^*)$.
(1) Find the general formula for the sequence $\{a_n\}$;
(2) Let $b_n = 2n a_n$, and the sum of the first $n$ terms of the sequence $\{b_n\}$ be $T_n$, find the expression for $T_n$.

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