
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 that $a\neq 0$, let set $A=\{x|x^{2}-x-6 < 0\}$, $B=\{x|x^{2}+2x-8\geqslant 0\}$, and $C=\{x|x^{2}-4ax+3a^{2} < 0\}$, and $C\subseteq(A\cap\neg_{R}B)$. Find the range of values for the real number $a$.

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