
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 the number of ordered triples $(x, y, z)$ of positive integers that satisfy $\text{lcm}(x, y) = 180, \text{lcm}(x, z) = 210, \text{lcm}(y, z) = 420$.
A) 2
B) 4
C) 6
D) 8

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