
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
Real numbers \(a, b, c\) satisfy the following system of equations:

\[
\left\{
\begin{array}{l}
\frac{ab}{a+b} = 2 \\
\frac{bc}{b+c} = 5 \\
\frac{ca}{c+a} = 9
\end{array}
\right.
\]

Find the value of the expression \(\frac{abc}{ab + bc + ca}\).

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