
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
(12 points) Let $A = \{x^2, 2x - 1, -4\}$ and $B = \{x - 5, 1 - x, 9\}$. Given that the intersection $B \cap A = \{9\}$,

(1) Find the value of $x$.
(2) Find the union $A \cup B$.

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