
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
It is known that $\{a_n\}$ is an arithmetic sequence, $\{b_n\}$ is a geometric sequence, and $b_2 = 3$, $b_3 = 9$, $a_1 = b_1$, $a_{14} = b_4$.  
(1) Find the general term formula for $\{a_n\}$.  
(2) Let $c_n = a_n + b_n$, calculate 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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