
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
In acute triangle $\triangle ABC$, the sides opposite the internal angles are $a$, $b$, $c$ respectively, and $a=1$, $b\cos A-\cos B=1$. If $A$ and $B$ vary, and $\lambda \sin B-\sin ^{2}A$ has a maximum value, then the range of positive number $\lambda$ is ______.

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