(1) Special discovery: As shown in figure 1, if point E and point F are the midpoints of DC and CB sides respectively, it is proved that the intersection point O of diagonal AC and BD of rhombic ABCD is the epicenter of equilateral △AEF;

(2) If point E and point F always move on the sides of DC and CB respectively, remember that the outer center of equilateral △AEF is p. 。

① conjecture verification: as shown in Figure 2, guess which straight line the epicenter P of △AEF falls on and prove it;

② Extended application: As shown in Figure 3, when E and F are the midpoint of DC and CB sides respectively, the intersection point P is regarded as a straight line, the DA side is at M point, the BC side is at G point, and the extension line of DC side is at N point. Please write directly? The value.

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