
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 the propositions \(p\): For any real number \(x\), the inequality \(ax^{2}+ax+1 > 0\) holds; \(q\): The equation \(x^{2}-x+a=0\) has real roots. If the proposition \(p \lor q\) is true, and the proposition \(p \land q\) is false, then the range of the real number \(a\) is _______.

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