
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
In the geometric sequence {a<sub>n</sub>}, the common ratio q > 0, the sum of the first n terms is S<sub>n</sub>, and S<sub>2</sub> = 3, S<sub>4</sub> = 15.
(1) Find the general term formula of the sequence {a<sub>n</sub>};
(2) Let b<sub>n</sub> = log<sub>2</sub>a<sub>n+1</sub>, if the sum of the first n terms of the sequence {b<sub>n</sub>} is T<sub>n</sub>, then is $b_{ n }^{ 2 }$, $2T_{n}$, $b_{ n+1 }^{ 2 }$ a geometric sequence? Explain your reason.

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