
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 positive numbers a, b, c, simplify the expression $\left(a+b+c+3\right)^{-1} \left(a^{-1} + b^{-1} + c^{-1}\right) \left(ab+bc+ca+3\right)^{-1} \left[\left(ab\right)^{-1} + \left(bc\right)^{-1} + \left(ca\right)^{-1}\right]$.

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