
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
Three distinct integers, $x$, $y$, and $z$, are randomly chosen from the set $\{1, 2, ..., 15\}$. What is the probability that $xyz - xy - xz - yz$ is divisible by 3?

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