A method implemented by one or more processors, the method comprising: receiving, by an automated assistant and from a given user via a client device associated with the given user, user input to initiate an assisted call; determining, by the automated assistant and based on the user input: an entity to engage with, on behalf of the given user, during the assisted call, and a task to be performed, on behalf of the given user, during the assisted call; determining, by the automated assistant and for one or more candidate parameters stored in association with the task and/or the entity, one or more corresponding values to be used in automatically generating synthesized speech, during the assisted call, in performing the task; initiating, by the automated assistant and using the client device associated with given user, performing of the assisted call; determining, by the automated assistant and during the performing of the assisted call and based on processing audio data, of the assisted call, that captures an utterance of an additional user associated with the entity, that information, associated with an additional parameter and which the automated assistant does not already know, is requested by the additional user; and in response to determining that the information associated with the additional parameter is requested: causing, by the automated assistant, the client device to render, outside of the assisted call, a notification that identifies the additional parameter, and that requests further user input for the information; wherein the method is characterized in that it comprises: prior to receiving any further input that is responsive to the notification, the automated assistant continuing the assisted call, wherein continuing the assisted call comprises rendering one or more instances of synthesized speech, as part of the assisted call for presentation at an additional client device of the additional user, that are based on one or more of the corresponding values for the candidate parameters that have already been determined by the automated assistant; determining, by the automated assistant and during continuing the assisted call, whether further user input, that is responsive to the notification and that identifies a particular value for the additional parameter, is received within a threshold duration of time; and in response to determining the further user input is received within the threshold duration of time: rendering, by the automated assistant, further synthesized speech, as part of the assisted call, that is based on the particular value. receiving, by an automated assistant and from a given user via a client device associated with the given user, user input to initiate an assisted call; determining, by the automated assistant and based on the user input: an entity to engage with, on behalf of the given user, during the assisted call, and a task to be performed, on behalf of the given user, during the assisted call; an entity to engage with, on behalf of the given user, during the assisted call, and a task to be performed, on behalf of the given user, during the assisted call; determining, by the automated assistant and for one or more candidate parameters stored in association with the task and/or the entity, one or more corresponding values to be used in automatically generating synthesized speech, during the assisted call, in performing the task; initiating, by the automated assistant and using the client device associated with given user, performing of the assisted call; determining, by the automated assistant and during the performing of the assisted call and based on processing audio data, of the assisted call, that captures an utterance of an additional user associated with the entity, that information, associated with an additional parameter and which the automated assistant does not already know, is requested by the additional user; and in response to determining that the information associated with the additional parameter is requested: causing, by the automated assistant, the client device to render, outside of the assisted call, a notification that identifies the additional parameter, and that requests further user input for the information; prior to receiving any further input that is responsive to the notification, the automated assistant continuing the assisted call, wherein continuing the assisted call comprises rendering one or more instances of synthesized speech, as part of the assisted call for presentation at an additional client device of the additional user, that are based on one or more of the corresponding values for the candidate parameters that have already been determined by the automated assistant; determining, by the automated assistant and during continuing the assisted call, whether further user input, that is responsive to the notification and that identifies a particular value for the additional parameter, is received within a threshold duration of time; and in response to determining the further user input is received within the threshold duration of time: rendering, by the automated assistant, further synthesized speech, as part of the assisted call, that is based on the particular value.