There are two firms in an industry producing a homogeneous product. The market demand function is given by \( P = 1 - (q_1 + q_2) \), where \( q_1 \) and \( q_2 \) are the output levels of Firm 1 and Firm 2, respectively. Firm 1’s cost function is common knowledge and equals zero. Firm 2’s cost function is private information. Firm 1 believes that Firm 2’s cost function is \( 0.5q_2 \) with probability 0.5 and that Firm 2’s cost function is \( 0.25q_2 \) with probability 0.5. The firms choose their quantities simultaneously. Let \( q_1^* \) denote the quantity produced by Firm 1 in the Bayesian Nash equilibrium of this game. Then, the value of \( 24q_1^* \) is _____________ (round off to one decimal place).