
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 real number $m$ satisfies $m^2 - 7ma + 12a^2 < 0$ ($a > 0$), and proposition q: The equation $\frac{x^2}{m-1} + \frac{y^2}{2-m} = 1$ represents an ellipse with foci on the y-axis. If $\neg p$ is a necessary but not sufficient condition for $\neg q$, find the range of values for the real number $a$.

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