
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 \\(n \in \mathbb{N}^*\\), in the expansion of \\(\left( x+2 \right)^n\\), the coefficient of the second term is \\(\frac{1}{5}\\) of the coefficient of the third term.  
(1) Find the value of \\(n\\);  

(2) If \\(\left( x+2 \right)^n = a_0 + a_1(x+1) + a_2(x+1)^2 + \cdots + a_n(x+1)^n\\), find the value of \\(a_1 + \cdots + a_n\\).

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