
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 \\((x+2)^{n}=a_{0}+a_{1}x+a_{2}x^{2}+\ldots+a_{n}x^{n} (n\in\mathbb{N}^*, n\geqslant 2)\\), and \\(a_{0}\\), \\(a_{1}\\), \\(a_{2}\\) form an arithmetic sequence.  
\\((1)\\) Find the middle term of the expansion of \\((x+2)^{n}\\);  
\\((2)\\) Find the sum of the coefficients of the odd powers of \\(x\\) in the expansion of \\((x+2)^{n}\\).

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