The gas-phase reaction between nitric oxide and chlorine is represented by the balanced equation
\[ 2\,\text{NO}(g) + \text{Cl}_2(g) \rightarrow 2\,\text{NOCl}(g) \]
A proposed mechanism for the reaction consists of two elementary steps:

Step 1 (fast equilibrium): \(\text{NO}(g) + \text{Cl}_2(g) \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} \text{NOCl}_2(g)\) \quad (\(k_1 = 2.0 \times 10^4 \text{ M}^{-1}\cdot\text{s}^{-1}\), \(k_{-1} = 5.0 \times 10^2 \text{ s}^{-1}\))

Step 2 (slow): \(\text{NOCl}_2(g) + \text{NO}(g) \xrightarrow{k_2} 2\,\text{NOCl}(g)\) \quad (\(k_2 = 5.0 \times 10^1 \text{ M}^{-1}\cdot\text{s}^{-1}\))

A reaction vessel at the same temperature is initially filled such that \([\text{NO}] = 0.020 \text{ M}\) and \([\text{Cl}_2] = 0.050 \text{ M}\). Based on the proposed mechanism, what is the initial rate of the reaction?