
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 $p:\forall x\in[\frac{1}{4},\frac{1}{2}]$, $2x < m(x^{2}+1)$, and $q:$ the function $f(x)=4^{x}+2^{x+1}+m-1$ has a zero point. If the proposition "$p$ and $q$" is true, then the range of values for the real number $m$ is _____.

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