
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 $\{a_n\}$ is an arithmetic sequence, the sum of its first $n$ terms is $S_n$, and $\{b_n\}$ is a geometric sequence, with $a_1 = b_1 = 2$, $a_4 + b_4 = 21$, and $S_4 + b_4 = 30$. (1) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(2) Let $c_n = a_n \cdot b_n$, where $n \in \mathbb{N}^*$, find the sum of the first $n$ terms of the sequence $\{c_n\}$.

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