
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
Let S\_n be the sum of the first n terms of the sequence {a\_n}, and S\_n = $\frac{3}{2}$(a\_n - 1) (n ∈ N*),
(1) Find the general term formula for {a\_n};
(2) The sequence {b\_n} satisfies b\_n = 1 + logₓa\_n, find the sum of the first n terms T\_n of {$\frac{1}{b\_n b_{n+1}}$}

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