
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 natural numbers \( x \) and \( y \) and an odd integer \( z \), it is known that \( x! + y! = 8z + 2017 \). Find all possible triples of numbers \( (x, y, z) \). (Recall that \( 1! = 1, 2! = 1 \cdot 2, n! = 1 \cdot 2 \cdot \ldots \cdot n \)). 

Answer: \( (1, 4, -249), (4, 1, -249), (1, 5, -237), (5, 1, -237) \).

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