
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 the sequence $\{a_n\}$ is an arithmetic sequence with $a_2=3$ and $a_4=7$; the sequence $\{b_n\}$ is a geometric sequence with a common ratio $q(q > 1)$, and satisfies the set $\{b_1,b_2,b_3\}=\{1,2,4\}$.
(Ⅰ) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$;
(Ⅱ) Find the sum of the first $n$ terms $S_n$ of the sequence $\{a_n+b_n\}$.

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