
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 the proposition p: The domain of the function $f(x) = \log(ax^2 - x + \frac{1}{16}a)$ is $\mathbb{R}$, and proposition q: The inequality $\sqrt{2x+1} < 1+ax$ holds for all positive real numbers $x$. If the proposition "p∨q" is true, and the proposition "p∧q" is false, determine the range of the real number $a$.

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