
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 $2x^2 + ax - a^2 = 0$ has a solution in the interval $[-1,1]$; proposition q: There is only one real number $x_0$ satisfying the inequality $x_0^2 + 2ax_0 + 2a \leq 0$. If the proposition “$p \lor q$” is false, find the range of the real number $a$.

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