
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 condition p: $A=\{x|2a\leq x\leq a^2+1\}$, condition q: $B=\{x|x^2-3(a+1)x+2(3a+1)\leq 0\}$. If condition p is a sufficient condition for condition q, find the range of the real number $a$.

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