
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 the function f(x) = x² + 2x, the sum of the first n terms of the sequence {a\_n} is S\_n, and the point (n, S\_n) (n ∈ N*) lies on the curve y = f(x).

1. Find the general term formula for the sequence {a\_n}.
2. Find the sum of the first n terms, T\_n, of the sequence {1/[a\_n(a\_n - 2)]}.

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