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

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