
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 a trapezoid  $ABCD$  with bases  $BC$  and  $AD$ , with  $AD=2 BC$ . Let  $M$  be the midpoint of  $AD, E$  be the intersection point of the sides  $AB$  and  $CD$ ,   $O$  be the intersection point of   $BM$  and  $AC, N$  be the intersection point of   $EO$  and  $BC$ . In what ratio, point  $N$  divides the segment  $BC$ ?

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