Nginx: try_fiiles directive with variable from path

I have set up a server block that looks like this:

root /var/www/platform

location / {
 index index.html;
}

location /contact {
 try_files $uri /contact.html;
}

This works fine. I can go to x.com/contact and the contact.html page loads.

Now I want to add a subdirectory products with files like product1.html and so on. When the user goes to x.com/products/product1 I want to load the html file.

Because the products subdir is within the platform directory, x.com/products/product1.html works fine with the current ^ setup. I just want to get rid of the need to have .html at the end.

So I try adding a location block

location /products/(product) {
 root /products;
 try_files /$1.html $1.html /index.html;
}

But obviously this doesn't work. Any help will be appreciated.

If there's another better (but still easy) approach, I'd love to know it too.

Richard basically answered the question in the comments (I am writing this to remove the question from the list of unanswered ones). The solution that worked is adding this location block instead:

location /products/ {
 try_files $uri $uri.html /index.html
}