
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
Let $\mathrm{ABC}$ be a triangle, and $\mathrm{O}$ a point inside this triangle. The line parallel to $(BC)$ passing through $O$ intersects $[CA]$ at $D$, the line parallel to $(CA)$ passing through $O$ intersects $[AB]$ at $E$, and the line parallel to $(AB)$ passing through $O$ intersects $[BC]$ at $F$. What is the value of the following sum of ratios?

$$
\frac{B F}{B C}+\frac{A E}{A B}+\frac{C D}{A C} ?
$$

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