
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 the positive geometric sequence be $\{a_n\}$ with $a_4=81$, and the arithmetic mean of $a_2$ and $a_3$ is $\frac{3}{2}(a_1+a_2)$.

  (I) Find the general formula for the sequence $\{a_n\}$;

(II) If $b_n=\log_3{a_{2n-1}}$, and the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n$, and the sequence $\{c_n\}$ satisfies $c_n=\frac{1}{4S_n-1}$, and $T_n$ is the sum of the first $n$ terms of the sequence $\{c_n\}$, if $T_n < \lambda n$ always holds, find the range of values for $\lambda$.

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