When ATC instructs you to climb immediately at the same time a TCAS resolution advisory states "Descend. Descend," what should you do?

When faced with a situation where Air Traffic Control (ATC) instructs you to climb immediately while your Traffic Collision Avoidance System (TCAS) issues a resolution advisory to descend, the appropriate action is to follow the TCAS advisory and descend.

TCAS is designed to provide alerts and guidance in potential collision situations, prioritizing safety by prompting the pilot to act on the resolution advisory provided. The system is continually monitoring the airspace around the aircraft, and its directives are based on real-time data that indicate the presence of conflicting traffic. When the TCAS advises a descent, it reflects a critical safety measure to avoid a potential airborne collision, which becomes paramount in this scenario.

Following the TCAS advisory is crucial because, in situations involving a conflict with other aircraft, avoiding a collision takes precedence over ATC instructions. Once the immediate threat has been resolved, the pilot should then communicate with ATC, informing them of the TCAS advisory and your actions. This way, ATC can provide further instructions based on the updated traffic situation.

In summary, the priority is given to TCAS advisories in the interest of safety, and the correct action is to descend.