
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 $\{a\_n\}$ that satisfies: $a\_1=1$, $a_{n+1} > a\_n (n∈N^{})$$, $a\_1+1$, $a\_2+1$, $a\_3+3$ form a geometric sequence, and $a\_n+2 \log _{2}b\_n=-1$.

1. Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. Find the sum of the first $n$ terms, denoted as $T\_n$, for the sequence $\{a\_n⋅b\_n\}$.

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