
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 of positive numbers \\({a_n}\\) with the sum of the first \\(n\\) terms as \\(S_n\\), it satisfies \\(a_n^2 = S_n + S_{n-1} (n \geq 2)\\), \\(a_1 = 1\\).

\\((1)\\) Find the general term formula of the sequence \\({a_n}\\).

\\((2)\\) Let \\(b_n = (1 - {a_n})^2 - a(1 - {a_n})\\), if \\(b_{n+1} > b_n\\) always holds for any \\(n \in \mathbb{N}^*\\), determine the range of the real number \\(a\\).

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