New to this - Need to close a gap in my setup to send emails

So i've just started automating my outreach. Here is what I'm doing:

Claude plugged into Lusha - This is allowing me to do some research based on my ICP and find very small targeted lists of 10-20 execs who I want to email. Claude then uses Lusha MCP to get the contact details

Claude into Hubspot - Claude checks for the contact and creates / updates

Claude drafts an email per person based on some research of the company and personalises

My gap is - I have to manually copy paste and send the email. Claude can't send from outlook via office365, nor can it seem to send from Hubspot. It also said it can't do sequences in Hubspot.

What do people recommend?

Ideally i'd like it to send the email from Hubspot so it's all there on the contact record, and create a task (easy) to follow up. Also ok to send from outlook which I can sync to Hubspot, then create teh task directly for follow up.