
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
Let $A = \{x \mid x^2 - 2x - 8 < 0\}$, $B = \{x \mid x^2 + 2x - 3 > 0\}$, $C = \{x \mid x^2 - 3ax + 2a^2 < 0\}$,
(1) Find $A \cap B$.
(2) Determine the range of the real number $a$ such that $C \subseteq (A \cap B)$.

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