How would I verify game cache files?
Right click a Source Engine game in your library, click Properties, click the Betas tab, click the drop-down menu and choose Steampipe beta (prerelease for CS:S), and once it says you've opted in, don't close the window down or Steam might forget your decision, while the properties window is still open, go to the Local Files tab and click 'Verify integrity of game cache...', you'll then be prompted with a message asking if you want to convert the game, choose yes (or OK or whatever the button is)
You must do this for each Source Engine game, one at a time, to ensure the game's contents will show up in Garry's Mod, these games you need to convert are Counter Strike: Source, Half Life 2, Half Life 2 Episode One, Half Life 2 Episode Two, and Portal
Team Fortress 2 is already on Steampipe (in non-beta form), so it does not require this action, and the contents of this game already work in Garry's Mod