
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 universal set $U=\mathbb{R}$, set $A=\{x|4^{x}>2\}$, and set $B=\left\{x\middle| \frac{x}{x+2}<0\right\}$  
(1) Find sets A and B.  
(2) If $M\cup (A\cup B)=\mathbb{R}$, and $M\cap (A\cup B)=\emptyset$, find the set M.

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