
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 solid cube has dimensions \(a \times b \times c\), where \(a\), \(b\), and \(c\) are integers and \(a \geq b \geq c \geq 1\). We know that \(4(ab + bc + ca) = 3abc\). Determine the number of ordered triples \((a, b, c)\).

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