
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
For \( x, y, z > 0 \), find the maximum value of the expression

\[ 
A = \frac{(x-y) \sqrt{x^{2}+y^{2}}+(y-z) \sqrt{y^{2}+z^{2}}+(z-x) \sqrt{z^{2}+x^{2}}+\sqrt{2}}{(x-y)^{2}+(y-z)^{2}+(z-x)^{2}+2} 
\]

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