Rolling Dice

A clan of ninjas found a peculiar map divided into squares approximately 0.5 \times 0.5 inches in size. In the middle, at a spot known as a pirate foothold, there is a square marked $1$. The adjacent squares from the north to the west are labeled $2$, $3$, $5$, and $4$, respectively. This unusual numbering puzzled the ninjas for a long time, until the cleverest among them realized it was related to dice: if the top shows $1$, and you roll (tilt) the die to the neighboring square on the right, $3$ will appear on top (depending, of course, on the orientation of the die). Alongside the map, they found a strange text initially attributed to the Bay Area Poets Coalition, though it seemed unlikely that even Joyce could have devised such a cryptic poem.

The first sentence reads "5X-YYX+Y.". They discovered its meaning:

• $X$ means one square to the east.

• $Y$ means one square to the north.

• $3X$ abbreviates $XXX$, and $3XYX$ means XXXYX.

A minus sign $-$ indicates the directions are reversed (east becomes west, north becomes south), while a plus sign $+$ restores the original directions. The sequence ends with a dot $.$. The number of dots appearing on the top face of the die in its final position signifies what can be found at that spot: a hut, a weapons cache, a well, or even a place of unspeakable horror.

Your task is to compute the coordinates of the final position (relative to the starting point) and determine the number of dots on the top face.