
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 $\\{a_{n}\\}$ with a common difference greater than $0$, $a_{3}$ and $a_{5}$ are the two roots of the equation $x^{2}-14x+45=0$.
(1) Find the general term formula of the sequence $\\{a_{n}\\}$;
(2) Denote $b_{n}=2^{a_{n}}+n$, find the sum of the first $n$ terms of the sequence $\\{b_{n}\\}$, $S_{n}$.

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