An electric fireplace cost a retailer $$451\mathrm{.}00$ less $24\frac{1}{3}\%,17\%,5\%.$ Markup is $42\%$ of the regular selling price. During the end$-$of$-$season sale, the electric fireplace is marked down $21\%.$

$($a$)$ What is the end$-$of$-$season sale price?

$($b$)$ What rate of markup based on cost will be realized during the sale?