
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 equation $\frac{x^2}{3+a} - \frac{y^2}{a-1} = 1$ represents a hyperbola, and proposition $Q$: The point $(2,a)$ is inside the circle $x^2 + (y-1)^2 = 8$. If $P \land Q$ is a false proposition, and $\neg Q$ is also a false proposition, find the range of the real number $a$.

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