
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: For all $x \in \mathbb{R}$, $ax^2 > -ax - 1$ ($a \neq 0$) always holds; proposition q: The circle $x^2 + y^2 = a^2$ is externally disjoint from the circle $(x + 3)^2 + (y - 4)^2 = 4$. If the proposition “$p \lor q$” is true, and “$p \land q$” is false, find the range of the real number $a$.

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