You come across scenarios wherein the send email tasks may fail. Below are few common error messages.
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The task 'Send Email' could not be executed.
Failed to send email using SMTP server 'smtp.server.com' from 'xyz@company.com' to 'abc@company.com'.
Reason: System.Net.Mail.SmtpException: The SMTP server requires a secure connection or the client was not authenticated. The server response was: 5.7.57 SMTP; Client was not authenticated to send anonymous mail during MAIL FROM [XXXXXXX.domain.com]

The execution of the job failed, server error: Task 3 'Send Email' failed with: Failed to send email using SMTP server 'XXXXXXX.domain.com' from 'xyz@company.com' to 'abc@company.com'.
Reason: System.Net.Mail.SmtpException: The SMTP server requires a secure connection or the client was not authenticated. The server response was: 5.7.1 Client was not authenticated

Task 3 Send Email failed\nSystem.Net.Mail.SmtpFailedRecipientException: Mailbox unavailable. The server response was: 5.7.1 Unable to relay for abc@company.com
at System.Net.Mail.SmtpTransport.SendMail(MailAddress sender, MailAddressCollection recipients, String deliveryNotify, Boolean allowUnicode, SmtpFailedRecipientException& exception)

All

- We need to configure Automation services to be able to send email tasks. To start with follow the KB article How to set SMTP and Send Email details
- If send email still fails, we can use TELNET to test email connectivity from the Node Manager machine (Automation Server) to the SMTP server.

Telnet (TN) is a networking protocol and software program used to access remote computers and terminals over the Internet or a TCP/IP computer network.
Perform the steps below from the Node Manager machine (Automation Server)
Step 1: Install the Telnet Client on your computer
Step 2: Find the FQDN or IP address of the destination SMTP server
Step 3: Use Telnet on Port 25 to test SMTP communication. SMTP port by default is 25. (Contact your local IT/Windows Team to know the exact SMTP details)
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C:\Windows\System32> telnet

Microsoft Telnet> set localecho
Microsoft Telnet> set logfile c:\TelnetTest.txt
Microsoft Telnet> OPEN mail1.fabrikam.com 25

220 mail1.fabrikam.com Microsoft ESMTP MAIL Service ready at Fri, 5 Aug 2016 16:24:41 -0700
EHLO contoso.com
250-mail1.fabrikam.com Hello [172.16.0.5]
250-SIZE 37748736
250-PIPELINING
250-DSN
250-ENHANCEDSTATUSCODES
250-STARTTLS
250-X-ANONYMOUSTLS
250-AUTH NTLM
250-X-EXPS GSSAPI NTLM
250-8BITMIME
250-BINARYMIME
250-CHUNKING
250 XRDST
MAIL FROM: chris@contoso.com
250 2.1.0 Sender OK
RCPT TO: kate@fabrikam.com NOTIFY=success,failure
250 2.1.5 Recipient OK
DATA
354 Start mail input; end with <CRLF>.<CRLF>
Subject: test
   
This is a test message.
.
250 2.6.0 <c89b4fcc-3ad1-4758-a1ab-1e820065d622@mail1.fabrikam.com> [InternalId=5111011082268, Hostname=mail1.fabrikam.com] Queued mail for delivery
QUIT
221 2.0.0 Service closing transmission channel
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NOTE:
If the recipient receives the email, it indicates that e-mail communication from the Node Manager machine (Automation Server) to the SMTP server is working as expected. Just in case the above steps do not help and give errors, you may need to loop in your local Windows/IT Team to get issue addressed.

This article will help you use the Telnet command to troubleshoot and check SMTP connectivity from the Node Manager machine (running Automation Services) to the SMTP server.

• Use Telnet to test SMTP communication on Exchange servers, Microsoft Learn 
  • https://technet.microsoft.com/en-us/library/bb123686(v=exchg.160).aspx