
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 that the terms of a geometric sequence $\{a_{n}\}$ are all positive, $S_{n}$ is the sum of the first $n$ terms of the geometric sequence $\{a_{n}\}$. If $a_{2}=\frac{2}{3}$ and $a_{3}a_{4}=2a_{6}$:
1. $S_{n} \lt t$ always holds. Find the minimum value of $t$.
2. Let $b_{n}=\frac{n}{a_{n}}$. Find the sum of the first $n$ terms of the sequence $\{b_{n}\}$ denoted by $T_{n}$.

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