
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 $M=\{x\mid-\frac{1}{2}<x<\frac{1}{2}\}$ and $N=\{x\mid x(x-1)\leqslant 0\}$, determine the value of $M\cup N$.

A) $[0,\frac{1}{2})$

B) $(-\frac{1}{2},1]$

C) $[-1,\frac{1}{2})$

D) $(-\frac{1}{2},0]$

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