
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
For the numbers \(a, b, c\), it is given that

$$
\frac{-a+b+c}{a}=\frac{a-b+c}{b}=\frac{a+b-c}{c}
$$

What values can the expression

$$
p=\frac{(a+b)(b+c)(c+a)}{abc}
$$

take?

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