
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
For the real number \( x \), consider the inequalities \( \left|x-\frac{(a+1)^{2}}{2}\right| \leq \frac{(a-1)^{2}}{2} \) and \( x^{2}-3(a+1) x + 2(3a+1) \leq 0 \) (where \( a \in \mathbb{R} \)). Let the solution sets of these inequalities be denoted by \( A \) and \( B \) respectively. Determine the range of values for \( a \) such that \( A \subseteq B \).

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