
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:
- \( p \) : The equation \( x^2 + m x + 1 = 0 \) has two distinct negative real roots.
- \( q \) : The equation \( 4x^2 + 4(m-2)x + 1 = 0 \) has no real roots.

Determine the range of the real number \( m \) such that \( p \) or \( q \) is true, but \( p \) and \( q \) are both false.

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