
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
Two propositions P: "For any real number $x$, $ax^2+ax+1>0$ always holds"; Q: "The equation $x^2-x+a=0$ has two distinct real roots". If $P\lor Q$ is true, and $P\land Q$ is false, then the range of real number $a$ is ______.

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