
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 an arithmetic sequence {a<sub>n</sub>} with a common ratio of q, it satisfies the conditions 2a<sub>1</sub>+a<sub>3</sub>=3a<sub>2</sub> and a<sub>3</sub>+2 is the middle term of the arithmetic sequence formed by a<sub>2</sub>, a<sub>4</sub>.
(1) Find q;
(2) If b<sub>n</sub>=a<sub>n</sub>log<sub>2</sub>a<sub>n</sub>, find the sum of the first n terms, S<sub>n</sub>, of the sequence {b<sub>n</sub>}.

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