At first,what does Juliet believe is the only solution to her problem? act 4

In Act IV, Scene 1, Juliet is talking to Friar Lawrence
about what she can do.  She does not want to marry Paris, but her parents are insisting
on it very strongly.

At that point, she thinks that her
best option or only option is to just go ahead and kill herself.  She tells Friar
Lawrence that she would rather die (she tells him all sorts of ways she'd rather die)
than marry Paris.  For example:

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O, bid me leap, rather than marry Paris,

From off the battlements of yonder
tower

It is at this point
that Friar Lawrence comes up with his idea about having her take that
potion.