
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 that the sequence \\(\{a_n\}\) is a non-zero arithmetic sequence and \\(S_n\) is the sum of its first \\(n\) terms, satisfying \\(a_n^2=S_{2n-1} (n\in\mathbb{N}^*)\), \\(b_n=a_n^2+\lambda a_n\). If \\(\{b_n\}\) is an increasing sequence, then the range of the real number \\(\lambda\) is           ;

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