Al is a medical doctor who conducts his practice as a sole proprietor. During $2023,$ he received cash of $$391,200$ for medical services. Of the amount collected, $$40,800$ was for services provided in $2022.$ At the end of $2023,$ Al had accounts receivable of $$99,900,$ all for services rendered in $2023.$ In addition, at the end of the year, Al received $$16,000$ as an advance payment from a health maintenance organization $($HMO$)$ for services to be rendered in $2024.$

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a$.$ Compute Al's gross income for $2023$ using the cash basis of accounting.

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