
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 $\left\{a_n\right\}$ is an arithmetic sequence, and $\left\{b_n\right\}$ is a geometric sequence, with $b_2=3$, $b_3=9$, $a_1=b_1$, and $a_{14}=b_4$.  
(1) Find the general formula for $\left\{a_n\right\}$.  
(2) Let $c_n=a_n+b_n$, find the sum of the first $n$ terms of the sequence $\left\{c_n\right\}$.

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