
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
Let the solution sets of the inequality $\left|x-\frac{(a+1)^{2}}{2}\right| \leqslant \frac{(a-1)^{2}}{2}$ and $x^{2}-3(a+1)x+2(3a+1) \leq 0$ (where $a \in \mathbf{R}$) be $A$ and $B$ respectively. If $A \subseteq B$, find the range of $a$.

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