
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: $x^2 + mx + 1 = 0$ has two distinct negative real roots, and q: the equation $4x^2 + (4m-2)x + 1 = 0$ does not have any real roots.
(1) If q is true, determine the range of the real number m;
(2) If p is true and q is false, determine the range of the real number m.

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