
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 propositions p: For any $x$, $ax^2 + ax + 1 > 0$ always holds true; q: The equation $x^2 - x + a = 0$ has real roots. If $p \vee q$ is a true statement and $p \land q$ is a false statement, find the range of values for the real number $a$.

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