A trader aims to manage the risks connected with gamma and vega in their portfolio, which comprises various options on a stock that does not pay dividends. The current portfolio displays a positive gamma and a negative vega. The trader has access to two at-the-money call options for the same stock, with one option expiring in 1 month and the other in 4 months. To effectively reduce the portfolio's gamma while increasing its vega, what specific strategy involving the purchase and sale of these two options should the trader implement?