
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; and $q$: the equation $x^{2}-x+a=0$ has real roots with respect to $x$. If $p \vee q$ is a true proposition and $p \wedge q$ is a false proposition, find the range of values for the real number $a$.

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