
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 a sequence \\(\left\{ a_n \right\}\\) where each term is positive and satisfies \\(a_1=1\\), \\(a_n^2-(2a_{n+1}-1)a_n-2a_{n+1}=0\\).  
\\((I)\\) Find \\(a_2, a_3\\);  

\\((II)\\) Find the general formula for \\(\left\{ a_n \right\}\\).

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