
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 set A<sub>n</sub> = {x > 0 | x = k<sub>1</sub>•2 + k<sub>2</sub>•2<sup>2</sup> + … + k<sub>n</sub>•2<sup>n</sup>}, where n ∈ ℕ*, n ≥ 2, k<sub>i</sub> ∈ {-1, 1} (i = 1, 2, …, n). Let S<sub>n</sub> denote the sum of all elements in the set A<sub>n</sub>.
(1) Find the values of S<sub>2</sub> and S<sub>3</sub>.
(2) Find S<sub>n</sub>.

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