
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 proposition $p$: $A=\{x\mid (4x-3)^{2}\leqslant 1\}$ and the proposition $q$: $B=\{x\mid a\leqslant x\leqslant a+1\}$. If $\lnot p$ is a necessary but not 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