
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
(1) Given the universal set $U=\{x|-5\leq x\leq 10, x\in \mathbb{Z}\}$, set $M=\{x|0\leq x\leq 7, x\in \mathbb{Z}\}$, $N=\{x|-2\leq x<4, x\in \mathbb{Z}\}$, find $(\complement_U N) \cap M$ (express the result both by descriptive method and listing method).  
(2) Given the universal set $U=A\cup B=\{0,1,2,3,4,5,6,7,8,9,10\}$, if $A\cap \complement_U B=\{2,4,6,8\}$, find the set $B$;  
(3) Given the set $P=\{x|ax^2+2ax+1=0, a\in \mathbb{R}, x\in \mathbb{R}\}$, when set $P$ has only one element, find the value of the real number $a$ and the element.

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