
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 $S\_n$ be the sum of the first $n$ terms of the arithmetic sequence ${a\_n}$, where $a\_1=1$, and $\frac{S\_n}{a\_n} = λa_{n+1}(n∈N^∗).$ Let $b\_n=\frac{a\_n}{3^n}$, and the sum of the first $n$ terms of the sequence ${b\_n}$ is $T\_n$. If for any $n≥k(k∈N^∗)$, we have $|T\_n−\frac{3}{4}|<\frac{1}{4n}$, then the minimum value of the constant $k$ is $\_\_\_\_\_\_\_\_$.

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