
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 universal set $U = \mathbb{R}$, let $M = \{ x | y = \log(1 - \frac{2}{x}) \}$ and $N = \{ x | y = \sqrt{x - 1} \}$. Find the intersection of $N$ and the complement of $M$ in $U$, denoted as $N \cap (\complement_U M)$.

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