
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 conditions $p:A=\left{ x\mid 2a\leqslant x\leqslant a^{2}+1 \right}$ and $q:B=\left{ x\mid x^{2}-3(a+1)x+2(3a+1)\leqslant 0 \right}$, find the range of values for the real number $a$ if condition $p$ is a sufficient condition for condition $q$.

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