
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 the sequence $\{ a_{n}\}$, where $a_{1}{=}1$ and $a_{n}{=}2a_{n{-}1}{+}1$ for $n{\geqslant }2$ and $n{∈}N^{{*}}$.

(1) Let $b_{n}{=}\log_{2}(a_{n}{+}1)$. Determine if $\{b_{n}\}$ is an arithmetic sequence and explain your reasoning.

(2) Under the conditions of (1), let $c_{n}{=}\frac{b_{n}}{a_{n}{+}1}$. Find the sum of the first $n$ terms of the sequence $\{ c_{n}\}$, denoted as $T_{n}$.

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