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Upon checking your account and form, I see that the standalone link (http://www.jotform.us/form/41263797742160) of your form works correctly in both Chrome, Firefox and IE, all with latest version.
The next thing that I checked is your website link where the JotForm is embedded, I was unable to see the Form Tabs widget in IE.
1. Here you will see that the widget "Form Tabs" is not displaying, this is the reason why you can't continue using the "Next" button.
2. But a couple of refresh fixes the problem and the Form Tabs are now showing.
I see that you are using Squarespace in building your website? May I know how you embedded your JotForm? I would suggest that you re-embed your form's code using this guide that we have: Adding Form To Squarespace. The guide shows that you will use an iFrame, the iframe code makes a good choice because if closes your form from other script codes that may conflict your widgets or your form's function.
Or you can also remove the "Form Tabs" widget if it is not that essential in your workflow process. But, please do try re-embedding first and see if that fixes that problem.