
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
In trapezoid  $ABCD$  holds  $AD \mid \mid BC$ ,  $\angle ABC = 30^{\circ}$ ,  $\angle BCD = 60^{\circ}$  and  $BC=7$ . Let  $E$ ,  $M$ ,  $F$  and  $N$  be midpoints of sides  $AB$ ,  $BC$ ,  $CD$  and  $DA$ , respectively. If  $MN=3$ , find  $EF$ 

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