
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. Find the set of all possible values of
\[ g(a,b,c) = \frac{a^2}{a^2 + b^2} + \frac{b^2}{b^2 + c^2} + \frac{c^2}{c^2 + a^2}. \]

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