
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 $p: 2a \leq x \leq a^2 + 1$, $q: x^2 - 3(a + 1)x + 6a + 2 \leq 0$, if $p$ is a sufficient condition for $q$, find the range of the real number $a$.

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