
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 proposition p be: For all $x\in\mathbb{R}$, the function $f(x) = \log(ax^2 - x + \frac{1}{16}a)$ is meaningful, and proposition q be: For all $x > 0$, the inequality $\sqrt{2x+1} < 1 + ax$ always holds. If the proposition "p or q" is true, and the proposition "p and q" is false, find the range of values for the real number $a$.

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