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**Reading Material:**
Nine-grade mathematics textbooks have the following passage:
"People call the number $\frac{\sqrt{5}-1}{2}$ the golden ratio. If a line segment is divided into two parts such that the ratio of the longer part to the whole segment is the golden ratio, then the ratio of the shorter part to the longer part is also the golden ratio."
According to the above text, if point $P$ divides a line segment into two parts such that the ratio of the longer part to the whole segment is the golden ratio, we call point $P$ the golden section point of this line segment.
**(1) Direct Application:**
As shown in Figure 1, line segment $AB=2$, and point $C$ is the golden section point of line segment $AB$, and $AC < BC$. Find the length of $AC$.
**Chart/Diagram Description (Figure 1):**
* **Type:** Line segment.
* **Main Elements:**
* **Points:** Two distinct points, A and B.
* **Lines:** A straight line segment connecting point A and point B.
* **Labels and Annotations:** "A", "B", "图 1" (Figure 1).
**(2) Analogous Application:**
As shown in Figure 2, on the number axis, point $O$ represents the number $0$, and point $E$ represents the number $2$. Draw $EF \perp OE$ from point $E$, and $EF = \frac{1}{2}OE$. Connect $OF$; with $F$ as the center and $EF$ as the radius, draw an arc intersecting $OF$ at $H$; then with $O$ as the center and $OH$ as the radius, draw an arc intersecting $OE$ at point $P$. Then point $P$ is the golden section point of line segment $OE$. The length of line segment $OP$ is ______, and the number represented by point $P$ on the number axis is ______.
**Chart/Diagram Description (Figure 2):**
* **Type:** Geometric construction diagram on a number line.
* **Main Elements:**
* **Coordinate Axes:** A horizontal number line with an arrow indicating the positive direction. The origin is marked as O and labeled "0". Another point E is marked and labeled "2".
* **Points:** O, E, P, H, F.
* **Lines:**
* Line segment OE (part of the number line).
* Line segment EF drawn vertically upwards from E, perpendicular to OE.
* Line segment OF connecting O and F.
* **Shapes:**
* A right angle symbol is shown at E, indicating $EF \perp OE$.
* An arc is drawn centered at F, passing through E and intersecting OF at H.
* Another arc is drawn centered at O, passing through H and intersecting OE at P.
* **Labels and Annotations:** "O", "0", "P", "E", "2", "H", "F", "图 2" (Figure 2).
**(3) Extension Application:**
In an acute isosceles triangle where $\frac{底}{腰} = \frac{\sqrt{5}-1}{2}$ (ratio of base to leg), it is called a "golden triangle". As shown in Figure 3, in parallelogram $ABCD$, $AB > 6$, $AD = \sqrt{5}+1$, $\angle A = 72^\circ$. Point $M$ is a moving point on line segment $AB$. If $\triangle DAM$ is an isosceles triangle with $\angle A$ as its base angle, explain why $\triangle DAM$ is a "golden triangle" and find the value of $AM$ at this time.
**Chart/Diagram Description (Figure 3):**
* **Type:** Geometric figure (parallelogram).
* **Main Elements:**
* **Shapes:** A quadrilateral named ABCD, which appears to be a parallelogram.
* **Points:** Vertices A, B, C, D.
* **Lines:** Line segments AB, BC, CD, DA forming the parallelogram.
* **Labels and Annotations:** "D", "C", "A", "B", "图 3" (Figure 3).
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