
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 $A=\{x|1\leqslant x < 6\}$, $B=\{x|5 < x < 10\}$, and $C=\{x|ax+1 > 0\}$.

(I) Find $A∪B$ and $(∁_{R}A)∩B$;

(II) If $A∩C=A$, find the range of values for the real number $a$.

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