How can strip index.php? but allow /?ACT to function?

Question

I'm using the following ht access file to strip index.php from my URLs

# secure .htaccess file
<Files .htaccess>
 order allow,deny
 deny from all
</Files>

ReWriteEngine on
RewriteBase /

ReWriteCond $1 !(img|safe-area|library-shelf|images|system|themes|index\.php) [NC]
ReWriteRule ^(.*)$ /index.php?/$1 [L]

This works for the server that I'm using, but the

ReWriteRule ^(.*)$ /index.php?/$1 [L]

means that functions such as login and logout don't work. I can force them to work by manually adding index.php.

So I guess a need to strip index.php? but not for www.site/?ACT=10 for example.

Any thoughts on what I can do?