
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
Let $a$ be a real number, and consider the proposition $p$: the solution set of the inequality $\left( \frac{1}{2}\right)^{|x|} \geqslant a$ is $\phi$, and the proposition $q$: the domain of the function $f(x)=\lg (ax^{2}+(a-2)x+ \frac{9}{8})$ is $\mathbb{R}$. If the proposition $p \lor q$ is true and the proposition $p \land q$ is false, find the range of values for $a$.

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