<image>As shown in the figure, in △ABC, it is known that ∠BAC=45°, AD is perpendicular to BC at D, BD=2, and DC=3. Find the length of AD.
Xiaoping ingeniously used the concept of reflection symmetry to transform the figure and cleverly solved this problem.
Please explore and solve the following questions according to Xiaoping's approach:
(1) Respectively using AB and AC as axes of symmetry, draw the reflection symmetry figures of △ABD and △ACD with D's symmetric points as E and F. Extend EB and FC to intersect at point G, and prove that quadrilateral AEGF is a square;
(2) Let AD=x, and using the Pythagorean theorem, establish an equation model in terms of x and find the value of x.

