
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 a sequence $\{a_{n}\}$ that satisfies $\frac{1}{a_1}+\frac{1}{2a_2}+\frac{1}{3a_3}+\ldots+\frac{1}{na_n}=\frac{n(n+3)}{4}$.  
$(1)$ Find the general formula for $\{a_{n}\}$.  
$(2)$ If $b_n=4^n(3n-1)a_n$, find the sum of the first $n$ terms of the sequence $\{b_{n}\}$ denoted as $T_{n}$.

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