
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 geometric sequence with positive terms \\(\{a_n\}\) whose sum of the first \\(n\\) terms is \\(S_n\\), if \\(S_4 = 120\\), and \\(3a_4\\) is the arithmetic mean between \\(a_6\\) and \\(-a_5\\),  
\\((1)\\) Find the general term formula for the sequence \\(\{a_n\}\);  
\\((2)\\) Suppose 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 value of \\(\sum_{i=1}^n \frac {1}{T_i}\\).

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