
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 $x,$ $y,$ $z$ be positive real numbers such that $z = \cos^2(\theta)$ for some angle $\theta$. Calculate the set of all possible values of the function:
\[ g(x, y, \theta) = \frac{x}{x+y} + \frac{y}{y+\cos^2(\theta)} + \frac{\cos^2(\theta)}{\cos^2(\theta) + x}. \]

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