
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 the statements $p$: $(4x-3)^2 \leqslant 1$ and $q$: $x^{2}-(2a+1)x+a(a+1) \leqslant 0$, if $\lnot p$ is a necessary but not sufficient condition for $\lnot q$,
1. What condition is $p$ for $q$?
2. Find the range of values for the real number $a$.

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