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

A) $(1,+\infty )$
B) $(1,2)$
C) $[0,2)$
D) $(0,1)$

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