
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]


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Given that ${S_n}$ is the sum of the first $n$ terms of the sequence ${{a_n}}$, and ${a_1=1}$, ${S_n+1=a_{n+1}}$ (${n\in\mathbb{N}^*}$).

(1) Find the general term formula for the sequence ${{a_n}}$.

(2) If the sequence ${{b_n}}$ satisfies ${{b_n}=\frac{n}{4{{a_n}}}}$, find the sum of its first $n$ terms, denoted as ${{T_n}}$.

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