
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
Determine all sets of six positive integers $\{a, b, c, x, y, z\}$ such that:

- $a \geq b \geq c$ and $x \geq y \geq z$
- $a + b + c = x + y + z$
- $x + y + z = a \times b \times c$

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