
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 $A=\{x|{x^2}-6x+8≤0\},B=\left\{{x\left|{\frac{x-1}{x-3}}\right.≥0}\right\},C=\{x|{x^2}-(2a+4)x+{a^2}+4a≤0\}$.<br/>$(1)$ Find $A\cap B$;<br/>$(2)$ If $A\subseteq C$, find the range of real number $a$.

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