
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
(1) Find the domain of the function $y= \sqrt {\sin x}+ \sqrt { \frac{1}{2}-\cos x}$.
(2) Find the range of the function $y=\cos ^{2}x-\sin x$, where $x\in\left[-\frac {\pi}{4}, \frac {\pi}{4}\right]$.

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