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

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