
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 that $p$: $\forall x \in \{ \frac{1}{4}, \frac{1}{2} \}$, $3x < m(x^{2}+1)$, and $q$: The function $f(x)=4^{x}+2^{x+1}+m-1$ has a zero point. If the statement "$p$ and $q$" is false, and "$p$ or $q$" is true, find the range of values for the real number $m$.

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