
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 the sum of its first $n$ terms denoted by $S_n$. It is also given that $a_5 = 3a_2$ and $S_7 = 14a_2 + 7$.

(I) Find the general term of the sequence $\{a_n\}$.

(II) If the sequence $\{a_n + b_n\}$ is a geometric sequence with first term 1 and common ratio 2, find the sum of the first $n$ terms, denoted by $T_n$, of the sequence $\{b_n(a_n + b_n)\}$.

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