
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
A sequence $\left\{a_{n}\right\}$ has a sum of its first $n$ terms denoted as $S_{n}$, and satisfies $a_{1}=1$, $2S_{n}=(n+1)a_{n}$. Another sequence $\left\{b_{n}\right\}$ is defined by $b_{n} = 2^{a_{n}+1}$.

(1) Find the general terms for the sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$.
(2) Find the sum of the first $n$ terms, denoted as $T_{n}$, for the sequence $\left\{\frac{1}{a_{n} \cdot (\log_{2}b_{n})}\right\}$.

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