
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
Find all integer tuples \((a, b, c, x, y, z)\) that satisfy:
(i) 
\[
\begin{cases}
a + b + c = xyz \\
x + y + z = abc
\end{cases}
\]
(ii) 
\[
a \geq b \geq c \geq 1, \quad x \geq y \geq z \geq 1
\]

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