
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 set $A = \{x | x^2 - 3x + 2 = 0\}$, and set $B = \{x | x^2 + 2(a + 1)x + (a^2 - 5) = 0\}$.
(1) If $A \cap B = \{2\}$, find the value of the real number $a$.
(2) If $A \cup B = A$, find the range of values of the real number $a$.

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