
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
The range of the function \( y = \frac{\sqrt{1 - x^2}}{2 + x} \) is \(\qquad\)
\[ \left[0, \frac{\sqrt{3}}{3}\right] \]

Given that \( x \in [-1, 1] \).

Let \( x = \cos \alpha (\alpha \in [0, \pi]) \). Then,
\[ y = \frac{\sin \alpha}{2 + \cos \alpha} (y \geqslant 0) \]

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