
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
Let \( x, y, z, w \) be real numbers such that \( x, y, z > 0 \) and \( w \geq 0 \). Find the set of all possible values of
\[ g(x, y, z, w) = \frac{x}{x+y} + \frac{y}{y+z} + \frac{z}{z+w} + \frac{w}{w+x}. \]

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