
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
Given the sets \( A=\{1,5\} \) and \( B=\{x^{2}-3x+1, x^{2}-4x+5\} \), if the number of elements in the set \( A \cup B \) is 3, then the real number \( x \) equals what?

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