I would like to know why you want to use apex:form in this page, if there is any specific reason please share so that we can think of any other way to achieve it. if your query was just to find a proper structure then above is your answer.
Salesforce Exapmle in Documentation is also like the same
You can't nest form tags from what I recall. If you want two different forms, just get rid of the parent form tag.
That is what your structure should be
I would like to know why you want to use apex:form in this page, if there is any specific reason please share so that we can think of any other way to achieve it. if your query was just to find a proper structure then above is your answer.
Salesforce Exapmle in Documentation is also like the same
I was trying to use a actionFunction component is the reason for the form tag