
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 proposition P be: A real number $x$ satisfies $2x^2 - 5ax - 3a^2 < 0$, where $a > 0$. Proposition Q is: A real number $x$ satisfies $$\begin{cases} 2\sin x > 1 \\ x^2 - x - 2 < 0 \end{cases}$$.
(1) If $a = 2$, and $p \land q$ is true, find the range of real numbers $x$.
(2) If $\lnot p$ is a sufficient but not necessary condition for $\lnot q$, find the range of real numbers $a$.

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