
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 propositions $p$ and $q$:
- Proposition $p$: The equation $x^{2}+mx+1=0$ has two distinct negative roots.
- Proposition $q$: The equation $4x^{2}+4(m-2)x+1=0$ has no real roots.
Find the range of real number $m$ that makes both propositions true.

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