
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 two propositions, \(P\): For any real number \(x\), \(ax^{2}+ax+1 > 0\) always holds; \(Q\): The equation \(x^{2}-x+a=0\) has real roots. If \(P \lor Q\) is true, and \(P \land Q\) is false, determine the range of the real number \(a\).

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