After you go through Fourrage Road to reach Coumarine City, you ride the monorail to reach Coumarine Gym.
Near the entrance of the gym, there is a vine for you to climb on to go toward the top of the gym's tower. Stand on the footprint symbol on the ground below the vine to grab onto it. You'll automatically climb up.
Don't go to the left from here: it's a dead end. Instead, if you go to the right, stand on the footprints and press A to swing across. On the other side, you find Pokémon Ranger Chaise, who has a level 32 Simisage.
Now go up the rope near the Pokémon Ranger that you just fought. At the top, stand on the nearby footprint symbol and press A to swing across. Go to the left and swing across again, then climb up the rope there.
Don't go up the rope to the area above you. It's a dead end. You can go to the right, but it's optional. If you do, you find Pokémon Ranger Maurice. He has a level 29 Ferroseed, a level 29 Lombre, and a level 29 Carnivine.
Go all the way to the left, then down the rope at the end. Down here, you find Pokémon Ranger Brooke. She has a level 30 Roselia and a level 30 Wormadam.
Near Brooke, go up the rope, then swing across the rope to the left by standing on the footprints and pressing A. Climb up the rope at the end. There is a dead end to the left, so go to the right until you reach Pokémon Ranger Twiggy. She has a level 29 Gloom and a level 31 Exeggutor.
Go up the rope from Twiggy, then go to the right until you reach Gym Leader Ramos. Talk to Ramos to start the battle.
Ramos has a level 30 Jumpluff, a level 34 Gogoat, and a level 31 Weepinbell. You receive the Plant Badge, which causes traded pokémon up to level 60 to obey you. It also allows you to use Fly outside of battle, which means that it will be easy for you to go back to Pokémon Centers that you've been to before. Ramos also gives you TM86 Grass Knot.
Ramos opens a gate that gives you a shortcut to the entrance of the gym. Just walk onto the slide and you'll go down to the entrance.
Go south from the Coumarine Gym and you will get a strange Holo Clip from Lysandre, urging you to use your Mega Evolution ability to make the world a better place.
Continue going south into the gate that leads to Route 13. You'll meet Sina and Dexio. They give you the Mountain Kalos Pokédex.
Now go south to reach Route 13: Lumiose Badlands.
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