In a magical forest, Somchai finds a peculiar artifact known as the Mirror of Inversion. This mirror has the property of showing everything as if it were horizontally flipped. While exploring its abilities, Somchai places the Mirror of Inversion at the edge of a clearing and looks into it. In the reflection, Somchai sees his friend Yukio approaching from behind. Yukio is holding a map with a red dot indicating a hidden treasure in the forest. In the mirror, Somchai notices that Yukio is using his left hand to hold the map and that the red dot is on the left side of the map. As Yukio draws near, Somchai turns around to greet him but is momentarily confused about which hand Yukio is using to hold the map and on which side of the map the red dot is located. Somchai is aware of the Mirror of Inversion's magical properties and knows that reflections in the mirror are not representative of real-world orientations. Interpret the spatial reasoning Somchai must apply to deduce where the red dot is on the map as Yukio approaches, and which hand Yukio is using to hold the map, using their POV (point of view) looking at each other and without Somchai looking back into the mirror.

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To resolve his confusion, Somchai must recall the properties of the Mirror of Inversion and the way it affects the images of objects. The mirror flips images along the vertical axis, thus what appears to be left in the reflection is actually right in reality, and vice versa. 

Starting with determining which hand Yukio is using to hold the map, Somchai saw Yukio in the mirror seemingly using his left hand. Since the mirror flips images horizontally, Somchai must infer that Yukio is actually holding the map with his right hand in reality. This is a straightforward inversion of left to right due to the horizontal flip introduced by the Mirror of Inversion.

Deciphering the location of the red dot on the map requires slightly more intricate reasoning. The mirror makes the red dot appear on the left side of the map within its reflection. Since the mirror flips the orientation horizontally, Somchai must infer that the red dot is actually on the right side of the map in reality. This maintains consistency with the inversion principle applied to Yukio's hands.

Now, as Yukio approaches, Somchai uses this reasoning to understand what he would observe in reality, without relying on the mirror's reflection. He anticipates that Yukio will be holding the map in his right hand and the red dot will be on the right side of the map. When he turns away from the mirror to face Yukio, this is exactly what Somchai sees: Yukio's right hand is holding the map, and the red dot indicating the hidden treasure is on the right side of the map from Somchai's perspective, opposite of how it appeared in the reflective world of the magical Mirror of Inversion.