
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
(I) Given that p: 2x^2 - 3x + 1 ≤ 0 and q: x^2 - (2a + 1)x + a(a + 1) ≤ 0, if ¬p is a necessary but not sufficient condition for ¬q, find the range of values for the real number a.
(II) Given that proposition p states that the equation $\frac{x^2}{2m} - \frac{y^2}{m - 1} = 1$ represents an ellipse with foci on the y-axis, and proposition q states that the eccentricity e of the hyperbola $\frac{y^2}{5} - \frac{x^2}{m} = 1$ is in the interval (1, 2). If p and q have and only have one true proposition, find the range of values for m.

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