
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 proposition $p$: "The equation $x^2+mx+1=0$ has two distinct negative roots", and proposition $q$: "The domain of the function $f(x)=\log_2(4x^2+4(m-2)x+1)$ is $\mathbb{R}$", if "$p \vee q$" is true and "$p \wedge q$" is false, find the range of the real number $m$.

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