What legal authority does Donald Trump have to carry out his administrative actions despite facing multiple lawsuits?

According to the discussion, Donald Trump possesses executive authority as part of his presidential powers that enables him to pursue his administrative agenda despite facing approximately 40 ongoing lawsuits. The speaker argues that the courts, being part of the executive branch, support Trump's legal standing to implement his policies and decisions. The legal challenges are characterized as politically motivated rather than having substantial legal merit. This suggests that Trump's executive authority remains intact and provides him with the constitutional power to continue governing and making administrative decisions, regardless of the volume of legal opposition he faces from various sources.