
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 that $n\in N\*,n\\geqslant 2,$ and ${{k}\_{1}},{{k}\_{2}},{{k}\_{3}},\\cdot \\cdot \\cdot ,{{k}\_{n}}\\in \\left\\{ -1,1 \\right\\},$ set $A=\\left\\{ x > 0|x={{k}\_{1}}\\cdot 2+{{k}\_{2}}\\cdot {{2}^{2}}+\\cdot \\cdot \\cdot +{{k}\_{n}}\\cdot {{2}^{n}} \\right\\}$. Denote $A\\left( n \\right)$ as the sum of all elements in set $A$. Express $A\\left( n \\right)$ in terms of $n$.

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