
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
How many ordered triples \((x, y, z)\) of positive integers satisfy \(\text{lcm}(x, y) = 48\), \(\text{lcm}(x, z) = 900\) and \(\text{lcm}(y, z) = 180\)?
A) 0
B) 1
C) 2
D) 3 
E) 4

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