
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 $S_n$ is the sum of the first n terms of an arithmetic sequence {a_n}, and $a_3=5$, $S_7=49$.  
(1) Find the general formula for the sequence {a_n};  
(2) Let $b_n=2^n+a_n$, find the sum of the first n terms of the sequence {b_n}, denoted as $T_n$.

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