
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 ${a_{n+1}} > {a_{n}}\ (n \in \mathbb{N}^{*})$, ${a_{1}}=1$. When the first three terms of the sequence are added to $1$, $1$, and $3$ respectively, they form a geometric sequence. Additionally, ${a_{n}}+2{\log_{2}}{b_{n}}=-1$.

(1) Find the general term formulas for the sequences $\{a_n\}$ and $\{b_n\}$.
(2) Find the sum of the first $n$ terms, denoted by ${T_{n}}$, of the sequence $\{a_{n} \cdot b_{n}\}$.

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