
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 the product \( a \cdot b \cdot c = 1 \), what is the value of the following expression?

$$
\frac{a}{a b + a + 1} + \frac{b}{b c + b + 1} + \frac{c}{c a + c + 1}
$$

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