
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 \\(\{a_n\}\) with the sum of its first \\(n\\) terms denoted as \\(S_n\\), where \\(a_1 = -\frac{2}{3}\\), and it satisfies \\(S_n + \frac{1}{S_n} + 2 = a_n (n \geqslant 2)\\).
\\((1)\\) Calculate \\(S_1\\), \\(S_2\\), \\(S_3\\), and \\(S_4\\);
\\((2)\\) Based on \\((1)\\), conjecture the expression for \\(S_n\\).

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