I would do this in a different way than the other posters. The best way to check someones activity is to ask the members. Since you have so many, that may be difficult, but spend a day or two looking at clan chat often and ask everyone to mention if they are active of not. The people who don't respond in 2-3 days should be marked as inactive, but don't kick them yet.
Ask if anyone in the clan knows them, since they might be on vacation, or friends of someone in the clan who can verify their current situation.
Finally, as mentioned by other posters, assuming it is not a brand new season, check their league, number of attacks and donations, with donations probably being the most important. Obviously, if it's 3 weeks into the season and they don't have a league and haven't responded to any of your queries in clan chat, they are probably inactive. The last thing to do before kicking them (if you really want to verify) is to check their base for destruction/tombstones/full collectors.
Unfortunately, you may end up kicking a few people that don't deserve it, but that's just how it goes as a clan leader. They can always rejoin/reapply later if they are really interested and put in their message that they were kicked incorrectly.