
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 $M=\left{ x\mid 2x-{{x}^{2}}\ge 0 \right}$ and $N=\left\{ x\mid y=\frac{1}{\sqrt{1-{{x}^{2}}}} \right\}$, find the intersection of $M$ and $N$, denoted as $M\cap N$.

A) $\left( -1,0 \right]$
B) $\left[ -1,0 \right]$
C) $\left[ 0,1 \right)$
D) $\left[ 0,1 \right]$

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