
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
Let $\{a_{n}\}$ be a sequence of positive terms in geometric progression, and let $S_{n}$ be the sum of the first $n$ terms. If $2S_{3}=6a_{1}+5a_{2}+a_{3}$, find:<br/>
$(1)$ the common ratio of the sequence $\{a_{n}\}$;<br/>
$(2)$ if $a_{1}=4$, and $\{b_{n}\}$ satisfies ${b}_{n}=\frac{n}{{a}_{n}}$, find the sum of the first $n$ terms of $\{b_{n}\}$ denoted by $T_{n}$.

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