I want to use the status manager on my local installation of Tomcat 7 but it asks for a password and I can't recall what it is. How do I reset it without reinstalling?

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You'll want to look at your conf\tomcat-users.xml file. Note, as it is says in that file you'll need to have a user with the role "manager-gui" to use those tools.
<user username="tomcat" password="tomcat" roles="manager-gui"/>