
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]


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Let the universal set be $U=\{1,2,3,4,5,6\}$. Using subsets of $U$, we can represent $6$-bit strings composed of $0$'s and $1$'s. For example, $\{1,3\}$ represents the $6$-bit string $101000$, where the first and third digits are $1$ and the rest are $0$. It is also defined that the empty set represents the string $000000$.
  
$(1)$ If $N=\{2,3,6\}$, then the $6$-bit string represented by $\complement _{U}N$ is ______.
  
$(2)$ If $B=\{5,6\}$ and the set $A\cup B$ represents the string $011011$, then the number of sets $A$ that satisfy the condition is ______.

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