How to leverage 1000 people for seo?

Hello.

I sell a product online that a lot of people love and will do things to get one for free. I run giveaways all the time like.... "Like this post" for a chance to win, along with Share this post.. etc..

I can easily get 1000 people to do a particular action for me, but when ever I do I don't see anything happening for my seo.. like if 1000 people like or share a post with a link to my website in it, using keywords i want to rank high for.. i dont see my page move up at all.. which i feel it should..

So my question is, if I could get 1000 real people to do something, what would be the best things they could do... that would help get me higher on the SE for a particular keyword?

The SEO world is tricky and not really something of much use to have strangers do the work for you. Social media would be a good idea, but that alone would not increase your rankings. If I had 1000 people willing to do anything, I would ask each of them to have a blog to point at least link to my main site.

Going off what AreYouReady said already..
Having them all create blogs that point to your site is a great idea, continuing off that, I would also have them each set up social media profiles at the top 10-20 sites if they have not already. Having them link from their social media profiles to their blogs, which link to your site. Depending on the number of keywords you are targeting, I would divide them up amongst the blog topics of your people. Having them create ongoing content, while alternating linking patterns would also help long term

To hell with using them for SEO. Have each person get 10 new people to opt into a CPA or CPL offer on your site.

EDIT:

Or just straight into your own opt-in. Give them a list of "interests" to pick from and build a new, big opt-in list each month.

CPA is the way for you man. You can get ranking with FB posts alone!