
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 $a \neq 0$, let $A = \{x \mid x^2 - x - 6 < 0\}$, $B = \{x \mid x^2 + 2x - 8 \geq 0\}$, and $C = \{x \mid x^2 - 4ax + 3a^2 < 0\}$, with $C \subseteq (A \cap \neg_R B)$. Find the range of the real number $a$.

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