
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 positive geometric sequence {a<sub>n</sub>}, where a<sub>1</sub> = 3, and -3a<sub>2</sub>, a<sub>3</sub>, a<sub>4</sub> form an arithmetic sequence.

1. Find the general term formula for the sequence {a<sub>n</sub>}.
2. If b<sub>n</sub> = log<sub>3</sub>(a<sub>n</sub><sup>2</sup>), find the sum of the first n terms, T<sub>n</sub>, for the sequence {$\frac{1}{b_n b_{n+1}}$}.

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