
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 \( x, y, z \in (0, +\infty) \) and \(\frac{x^2}{1+x^2} + \frac{y^2}{1+y^2} + \frac{z^2}{1+z^2} = 2 \), find the maximum value of \(\frac{x}{1+x^2} + \frac{y}{1+y^2} + \frac{z}{1+z^2}\).

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