You just graduated from college and are starting your new job. You realized the importance to save for the future and have figured out that you will save $$1,000$ per month for the next $12$ years; and then increase to $$6,000$ per month for the following $6$ years. The amount accumulated at the end of these investments will be your retirement egg nest. You plan to start retirement and start withdrawing monthly amounts the following month $($you will be in retirement for $23$ years$).$ If your required rate of return is $12\%$ compounded monthly, how much are your monthly withdrawals?