
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
If there exist constants $k$ ($k \in \mathbb{N}^*$, $k \geq 2$), $q$, and $d$, such that the infinite sequence $\{a_n\}$ satisfies
$$
a_{n+1}= 
\begin{cases} 
a_{n}+d, & \frac{n}{k} \notin \mathbb{N}^* \\ 
qa_{n}, & \frac{n}{k} \in \mathbb{N}^*
\end{cases}
$$
then the sequence $\{a_n\}$ is called a "segment-ratio-difference sequence", where the constants $k$, $q$, and $d$ are respectively called the segment length, segment ratio, and segment difference. Let the sequence $\{b_n\}$ be a "segment-ratio-difference sequence".

(1) If the first term, segment length, segment ratio, and segment difference of $\{b_n\}$ are respectively 1, 3, $q$, and 3.  
① When $q=0$, find $b_{2016}$;  
② When $q=1$, let the sum of the first $3n$ terms of $\{b_n\}$ be $S_{3n}$. If the inequality $$S_{3n} \leq \lambda \cdot 3^{n-1}$$ always holds for $n \in \mathbb{N}^*$, find the range of values for the real number $\lambda$;  
(2) Suppose $\{b_n\}$ is a geometric sequence, and its first term is $b$. Write out all possible sequences $\{b_n\}$ that meet the conditions, and explain the reasons.

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