
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
Given the sets $M=\left\{ y \left\lvert\, y=x^{\frac{1}{2}} \right., x \in[1,4]\right\}$ and $N=\left\{ x \mid y=\log_{2}(1-x) \right\}$, find the set $M \cap \left(\complement_{\mathbf{R}} N\right)$.

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