
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
Through an internal point  $O$  of  $\Delta ABC$  one draws 3 lines, parallel to each of the sides, intersecting in the points shown on the picture.

![Image](http://www.mathlinks.ro/Forum/album_pic.php?pic_id=289)

Find the value of  $\frac{|AF|}{|AB|}+\frac{|BE|}{|BC|}+\frac{|CN|}{|CA|}$ .

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