
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
If \(\frac{(a-b)(b-c)(c-a)}{(a+b)(b+c)(c+a)}=\frac{2004}{2005}\), find \(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\).

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