
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
The full score of this problem is 10 points. Given the sets $A = \{2, 4, a^3 - 2a^2 - a + 7\}$ and $B = \{-4, a+3, a^2 - 2a + 2, a^3 + a^2 + 3a + 7\}$, if the intersection $A \cap B = \{2, 5\}$, find the value of the real number $a$ and the union $A \cup B$.

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