
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 monotonically increasing geometric sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$. It is known that $S_3=39$ and that $3a_4$ is the arithmetic mean between $a_6$ and $-a_5$.
(Ⅰ) Find the general term formula for the sequence $\{a_n\}$;
(Ⅱ) If another sequence $\{b_n\}$ satisfies $b_n=\log_3 a_{2n+1}$, and the sum of the first $n$ terms of $\{b_n\}$ is $T_n$, find the sum $\sum_{i=1}^{n} \frac {1}{T_i}$.

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