
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
Given that the sum of the first 9 terms of the sequence $\{a_{n}\}$ is 153, and the point $P(a_{n}, a_{n+1}) (n \in \mathbb{N}^{*})$ lies on the line $x - y + 3 = 0$.

(1) Find the general term formula of the sequence $\{a_{n}\}$:

(2) From the sequence $\{a_{n}\}$, take out the 2nd term, the 8th term, the 24th term, ..., and the $n \cdot 2^{n}$th term, in that order, to form a new sequence $\{b_{n}\}$. Find the sum of the first $n$ terms of the sequence $\{b_{n}\}$, denoted as $S_{n}$.

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