
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
Given that \(a, b, c\) are all non-zero real numbers, and \(ab = 3(a + b)\), \(bc = 4(b + c)\), and \(ac = 5(a + c)\), find the values of \(a\), \(b\), and \(c\).

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