
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 \( a, b, c \) be positive real numbers. Determine the set of all possible values of
\[ g(a, b, c) = \frac{a}{a + b} + \frac{b}{b + c} + \frac{c}{c + a}. \]

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