
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 that the domain of the function $f(x) = \frac{1}{\sqrt{1-x}}$ is $M$ and the domain of the function $g(x) = \log(1+x)$ is $N$, determine the option that best describes the relationship between $M$ and $N$.

A) $M \cap N = (-1, 1]$
B) $M \cap N = \mathbb{R}$
C) $\complement_{\mathbb{R}} M = [1,+\infty)$
D) $\complement_{\mathbb{R}} N = (-\infty,-1)$

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