
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 propositions $p$: the real number $m$ satisfies $m^2 - 7am + 12a^2 < 0$ (with $a > 0$), and $q$: the real number $m$ corresponds to an ellipse with foci on the y-axis represented by the equation $\frac{x^2}{m-1} + \frac{y^2}{6-m} = 1$.  
(1) When $a=1$, if proposition $p \land q$ is true, determine the range of $m$.  
(2) If $\neg q$ is a sufficient but not necessary condition for $\neg p$, determine the range of $a$.

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