
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 arithmetic geometric sequence {a<sub>n</sub>}, where a<sub>1</sub> = $$\frac {1}{2}$$, and a<sub>2</sub>, a<sub>3</sub>, a<sub>4</sub> - 1 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>2</sub>a<sub>n</sub><sup>2</sup> + 4, 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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