
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 propositions $p: \forall x \in (0, +\infty), (\frac{1}{2})^x + m - 1 < 0$ and $q: \exists x \in (0, +\infty), mx^2 + 4x - 1 = 0$, find the range of real number $m$ such that the proposition "p and q" is true.

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