
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 function $f(x) = a^2x^2 + ax - 2$ has a root in the interval $[-1, 1]$"; proposition Q: "There is only one real number $x$ satisfying the inequality $x^2 + 2ax + 2a \leq 0$". If either proposition P or Q is false, find the range of the real number $a$.

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