
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 sequence $\{a_n\}$ is a geometric sequence, and $a_2=1$, $a_5=27$, and $\{b_n\}$ is an arithmetic sequence, with $b_1=a_3$, $b_4=a_4$.
$(I)$ Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.
$(II)$ Let the sum of the first $n$ terms of sequence $\{b_n\}$ be $S_n$, find the sum of the first $n$ terms of the sequence $\left\{ \frac{2}{S_n} \right\}$, denoted as $T_n$.

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