
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
A right tetrahedron block has the numbers 1, 2, 3, and 4 written on its four faces. When three such tetrahedron blocks are tossed onto a table, let the numbers on the faces touching the table be $x$, $y$, and $z$.  
(1) Find the probability that $x+y+z=6$;  
(2) Find the probability that $xyz$ is divisible by 3.

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