He slams his way out of the back door, with no more plan than to start looking and not stop until he's found her. The beast itself is secondary at this point; he wants Alex back, and he'll do what he has to to make it happen.
He starts with a cursory look around the lake. It's just to rule it out; no animal is going to linger around an exposed space on its own, especially when its so popular with humans. So when that's done, he heads to the forest. It isn't that cold anymore, but the wind is getting up something fierce, and it's going to rain any minute. He doesn't give a toss. Let it rain.
The problem with the forest is that it's bloody massive, and even in his rage, he knows there's next to no chance of just stumbling across the thing when he's out here on his own. A couple of hours later, he's hot and wet through, and more furious than before. He stops to rest his back against a tree, and wipe water off his face. This isn't working. Maybe try somewhere where a bloke on his own has got more chance. He can always go back and recruit help for the woods later. So, he takes a bridle path he's familiar with, and walks on towards the mountains. He shoves his hands in his pockets, and buries his chin in his collar - and because of that, he almost misses the shadow that crosses the path up ahead. Almost.
His gun is in his hand half a second later. For once, he doesn't shout. If this is what he's looking for, he's not about to scare it off now.