
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 proposition $p$: The real number $x$ satisfies $x^2 + 4ax + 3a^2 < 0$, where $a \neq 0$; and proposition $q$: The real number $x$ satisfies $\begin{cases} x^2 - 6x - 72 \leq 0 \\ x^2 + x - 6 > 0 \end{cases}$.

(1) If $a = -1$ and $p \implies q$ is true, find the range of $x$;

(2) If $\lnot p$ is a necessary but not sufficient condition for $\lnot q$, find the range of $a$.

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