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

$$
\left\{\begin{array}{l}
\frac{a b}{a+b}=4 \\
\frac{b c}{b+c}=5 \\
\frac{c a}{c+a}=7
\end{array}\right.
$$

Find the value of the expression \(\frac{a b c}{a b + b c + c a}\).

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