Hotmail wants me to send new/old password to verify that it's actually me: do I follow through?

Recently, I got an email from the Hotmail Support Staff.and they said this (down below) --> So should I actually send them my password or is this fake?It appears as though your account has undergone numerous password change as well as a security answer change attempts in the last 24-72 hours . As a precautionary procedure, we would like you to change your password and reply to this email with your old and new password like the example below:Old Password:New Password: This will help verify that you are the correct user of this account. If the information provided does not match our system or if this email is not replied to then we will be forced to close this account for security purposes within a monitored time frame.Windows Live Hotmail Password Support Staff

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