
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 the following conditions hold:
$$
ab = 2(a+b), \quad bc = 3(b+c), \quad ca = 4(a+c).
$$

Find the value of \(a + b + c\).

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