
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 $a_{n+1}^2=a_na_{n+2}$, and $a_1= \frac{1}{3}$, $a_4= \frac{1}{81}$.  
(1) Find the general formula for the sequence $\{a_n\}$.  
(2) Let $f(x)=\log_3x$, $b_n=f(a_1)+f(a_2)+\ldots+f(a_n)$, $T_n= \frac{1}{b_1}+ \frac{1}{b_2}+\ldots+ \frac{1}{b_n}$, find $T_{2017}$.

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