
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 $S_n$ being the sum of its first $n$ terms, and $a_5 = 3a_2$, $S_7 = 14a_2 + 7$.
(I) Find the general formula for the sequence $\{a_n\}$.
(II) If the sequence $\{a_n + b_n\}$ is a geometric sequence with the first term 1 and common ratio 2, find the sum $T_n$ of the first $n$ terms of the sequence $\{(-1)^n b_n (a_n + b_n)\}$.

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