
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
Let $M = \{x | x^2 > 4\}$, and $N = \{x | 1 < x \leq 3\}$. Find the intersection of set $N$ with the complement of set $M$ in the set of real numbers.

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