
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 $M=\{x|y= \sqrt{4-x^{2}}, x\in \mathbb{Z}\}$ and $N=\{y|y=3^{x+1}, x\in \mathbb{R}\}$, find the number of proper subsets of $M \cap N$.

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