
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
Consider an arithmetic sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$. Given that $a\_2 + a\_4 = 6$ and $S\_4 = 10$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $b\_n = a\_n \cdot 2^n, (n \in \mathbb{N}^*)$. Find the sum of the first $n$ terms for the sequence $\{b\_n\}$, denoted as $T\_n$.

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