The gas-phase oxidation of nitric oxide is represented by the following overall equation:

\[ 2\,\text{NO}(g) + \text{O}_2(g) \rightarrow 2\,\text{NO}_2(g) \]

A researcher proposes the following two-step mechanism for the reaction:

Step 1 (fast equilibrium): \(2\,\text{NO}(g) \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} \text{N}_2\text{O}_2(g)\)

Step 2 (slow): \(\text{N}_2\text{O}_2(g) + \text{O}_2(g) \xrightarrow{k_2} 2\,\text{NO}_2(g)\)

The rate constants for the elementary steps are \(k_1 = 4.0 \times 10^3\text{ M}^{-1}\text{s}^{-1}\), \(k_{-1} = 2.0 \times 10^4\text{ s}^{-1}\), and \(k_2 = 3.0 \times 10^2\text{ M}^{-1}\text{s}^{-1}\). Based on the proposed mechanism, what is the initial rate of the reaction when \([\text{NO}] = 0.020\text{ M}\) and \([\text{O}_2] = 0.050\text{ M}\)?