
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 that statement p: the equation $x^2 - 2x + \frac{1}{2}m = 0$ has real roots, and statement q: the equation $\frac{x^2}{m+3} + \frac{y^2}{4} = 1$ represents an ellipse with foci on the x-axis, if both p and q are true, find the range of values for the real number $m$.

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