
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

Simplify the following expressions:

a) \( K = \sqrt{x + 2y \sqrt{x - y^2}} + \sqrt{x - 2y \sqrt{x - y^2}} \)

b) \( L = \frac{2xyz}{\sqrt{(1 + x^2)(1 + y^2)(1 + z^2)}} \), given that \( xy + yz + zx = 1 \)

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