
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 $p$ denotes the equation $\frac{x^{2}}{m-1} + \frac{y^{2}}{2-m} = 1$ represents an ellipse with foci on the $y$-axis, and $q$ denotes that the real number $m$ satisfies $m^{2} - (2a + 1)m + a^{2} + a < 0$ and $\lnot q$ is a sufficient but not necessary condition for $\lnot p$, find the range of values for the real number $a$.

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