
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 the sum of the first $n$ terms denoted as $S_n$, it is known that $S_4=24$ and $S_7=63$.

(1) Find the general term formula for the sequence $\{a_n\}$;

(2) If $b_n=2^{a_n} + (-1)^n \cdot a_n$, find the sum of the first $n$ terms, $T_n$, of the sequence $\{b_n\}$.

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