
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 $p$: "$1\leqslant x\leqslant 5$ is a sufficient but not necessary condition for $x^{2}-(a+1)x+a\leqslant 0$", and proposition $q$: "There are two triangles $\triangle ABC$ that satisfy $AC=6$, $BC=a$, and $\angle CAB=30^{\circ}$". If the proposition $\lnot p\land q$ is true, find the range of values for the real number $a$.

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