
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 with respect to x;
(1) What kind of condition is "a=0" for P?
(2) If only one of P and Q is true, find the range of real number a.

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