
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 $x>0$, $y>0$, $a=x+y$, $b= \sqrt{x^{2}-xy+y^{2}}$, $c=\lambda \sqrt{xy}$, if $a$, $b$, $c$ can be the lengths of the sides of a triangle, then the range of the positive real number $\lambda$ is \_\_\_\_\_\_.

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