J.F.Kennedy.
" It (Castro regime) will be prevented by whatever means may be necessary from taking action against any part of the Western Hemisphere,"

As far as is known, Kim doesn't have the capability to put a nuclear warhead on a missile yet.

As far as is known, he could well have. It is quite possible they already have it. If they do not they soon will have.

Firstly, it's not just about American people,

Trump's first duty is to protect American people.

The US has history in NK

The war stopped over 60 years ago. There have been no hostile acts against NK in all that time.
NK has been given no reason to fear invasion.

For a start, stop using intentionally inflammatory language whilst demonstrating a bellicose attitude.

The intentionally inflammatory language and bellicose attitude came from NK. Trump said they would be attacked if they continued to threaten nuclear strikes on Americans. Any President would.

use economic sanctions

They have been used. NK just ignored them and China undermined them.

try to persuade the Chinese to put pressure on the NK leadership.

That has been tried too. It has achieved nothing so far, and now time has run out.

At the end of the day, the only way to solve these issues is to TALK.
NK does not want to talk.

the exact range of the missiles is untested and speculative.

The assessment is that major US cities are in range.
Happy with that?