
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 \\(\{a_n\}\) with the sum of its first \\(n\\) terms denoted as \\(S_n.\\) If \\(3S_3=2S_2+S_4\\) and \\(a_5=32,\\)  
\\((1)\\) find the general formula for the \\(n\\)-th term of the sequence \\(\{a_n\};\\)  
\\((2)\\) let \\(b_n= \dfrac {1}{\log _{2}a_n\cdot \log _{2}a_{n+2}},\\) find the sum of the first \\(n\\) terms of the sequence \\(\{b_n\},\\) denoted as \\(T_n.\\)

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