What should be done if engine out mode is activated?

When the engine out mode is activated, disengaging the autothrottle and monitoring flight control is the appropriate response. This mode indicates that an engine has failed or is not providing the necessary thrust, requiring the pilot to take manual control of the aircraft's speed and handling. By disengaging the autothrottle, the pilot can ensure that they are directly managing throttle inputs according to the current aircraft performance characteristics and needs in this emergency state.

Monitoring flight controls is essential in this scenario to assess any alterations in the aircraft's handling and performance, as the loss of thrust from one engine can lead to asymmetrical flight forces. By being fully aware of the aircraft's behavior and responding appropriately, the pilot can maintain control and perform any necessary corrections or adjustments to recover from the situation safely.

The other responses would not adequately address the critical need for manual control and awareness during an engine out mode. Increasing throttle immediately may not be possible if the autothrottle is engaged and the thrust is not available. Turning off all navigation systems would further complicate an already challenging situation, and reducing airspeed progressively without controlling the aircraft's thrust can lead to loss of control during such an emergency.