
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 $p$: $2x^2 - 3x + 1 \leqslant 0$, and proposition $q$: $x^2 - (2a + 1)x + a(a + 1) \leqslant 0$. If $\lnot p$ is not a necessary and sufficient condition for $\lnot q$, find the range of values for the real number $a$.

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