The reversible reaction between nitrogen dioxide and dinitrogen tetroxide is represented by the following equation:

\[ 2\text{NO}_2\text{(g)} \rightleftharpoons \text{N}_2\text{O}_4\text{(g)} \]

A mixture of \(\text{NO}_2\text{(g)}\) and \(\text{N}_2\text{O}_4\text{(g)}\) is initially at equilibrium inside a rigid cylinder fitted with a movable piston at a constant temperature (State 1). The piston is then pushed downward to reduce the volume to half its original value at the same temperature, resulting in the non-equilibrium mixture shown in State 2. Which of the following statements best explains how and why the system responds as it proceeds to establish a new equilibrium?