
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 $A=\{x|-3 < x < 4\}$, $B=\{x|x^{2}+2x-8 > 0\}$, and $C=\{x|x^{2}-4ax+3a^{2} < 0, a\neq 0\}$,
(I) Find $A\cap(\lnot_{R}B)$;
(II) If $C\subseteq A$, determine the range of values for the real number $a$?

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