
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 an arithmetic sequence $\{a_n\}$, it is known that $a_4=14$ and the sum of the first 10 terms $S_{10}=185$.

(1) Find the general term formula $a_n$ for the sequence $\{a_n\}$.
(2) Let $\{b_n\}$ be a geometric sequence with the first term equal to 1 and a common ratio of 2. Find the sum of the first $n$ terms $S_n$ for the sequence $\{a_n+b_n\}$.

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