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I find doing bounties the quickest thing to do. Get ones related to patrol (complete X patrol missions on XXX) and general ones (Kill 100 enemies.....melee kill 20 enemies.....). Then load up patrol and travel from area to area (on earth is quickest) and just do them as a grind. You get 50 or 100 vanguard reputation for each bounty you do and you get 20/25 for each patrol mission (if you are quick and use sparrow you can burn through these). Hope that helps!