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Venezuela's future with the U.S. after the stunning capture of Nicolás Maduro largely hinges on Delcy Rodríguez, the vice president turned de-facto leader.The big picture: President Trump said the U.S. will run Venezuela and claimed Rodríguez, who also serves as the nation's oil minister, seemed cooperative, but her public address tells a different story.Behind the scenes: The New York Times reported that Trump's team backed Rodríguez as an acceptable solution for now, impressed by the English-speaking leader's handling of the oil industry.The snub: Trump explicitly sidelined opposition leader María Corina Machado, who won the Nobel Peace Prize last year and had dedicated the award to him.Trump said Machado didn't have the respect of the nation necessary to lead it.Context: Trump told reporters Saturday the U.S. will run Venezuela, but he said the close Maduro ally had spoken at length with Secretary of State Marco Rubio and appeared "willing to do what we think is necessary to make Venezuela great again.""I think she was quite gracious, but she really doesn't have a choice," the president said, telling media she told Rubio, "We'll do whatever you need."He told the New York Post that whether U.S. troops are stationed in Venezuela depends on if Rodríguez does what Washington wants.Yes, but: Rodríguez struck a sharp tone in her televised address following Maduro's seizure, saying the nation will never again be "slaves" or "the colony of another empire."She insisted "there is only one president in Venezuela, and his name is Nicolás Maduro."Where is Delcy Rodríguez, and who is in charge?It was not immediately clear where Rodríguez was in the aftermath of the attack — but Reuters, citing four sources familiar with her movements, reported Saturday that she was in Russia.However, Russian officials dismissed that report as false to state-owned media.The New York Times reported Saturday that she was in Caracas, according to three people close to her, noting that multiple other top Maduro allies appeared to have survived the attack.Catch up quick: Venezuela's Supreme Court ordered Rodríguez to assume the powers of acting president. She appeared in front of a Venezuelan flag in her first on-camera appearance after the address, demanding the release of Maduro.What they're saying: Trump ally and Senate Intelligence Committee Chair Tom Cotton (R-Ark.) said on CNN's "State of the Union" Sunday that the U.S. does not recognize Rodríguez as the legitimate leader of Venezuela, just as it did not recognize Maduro."I don't think that we can count on Delcy Rodríguez to be friendly to the United States until she proves it," he said.What to know about Rodríguez's political careerRodríguez, who Maduro also named the country's oil minister in 2024, has long been a key figure in chavismo, the political movement spearheaded by former President Hugo Chávez.The 56-year-old Caracas native studied law at the Central University of Venezuela. She ascended through the country's political ranks alongside her brother, Jorge Rodríguez, the president of the National Assembly. The siblings' father, Jorge Antonio Rodríguez, was a leftist guerrilla fighter who founded the Liga Socialista party and died in custody in the 1970s.Flashback: She's held various government positions, including serving as minister for communication and information from 2013 to 2014, foreign minister from 2014 to 2017 and recently as finance minister.As foreign minister, she made headlines in 2016 by trying to force her way into a Mercosur meeting after Venezuela was suspended from the trade group. Upon leaving the post, Maduro called her a "tiger" for her defense of his government.Naming Rodríguez as vice president in 2018, Maduro described her as a "young woman, brave, seasoned, daughter of a martyr, revolutionary and tested in a thousand battles," per Reuters.What has Rodríguez said about U.S. attacks?She forcefully condemned the Trump administration's operation and shared a statement from the government describing it as an attempt to seize Venezuela's resources."What is being done to Venezuela is a barbarity," she said, per The New York Times.Rodríguez has shared a series of government statements throughout the tightening of the U.S. squeeze on Maduro, accusing the U.S. of following a model of colonialism and violating international law.In an Instagram post rebuking Trump's order to block sanctioned oil tankers leaving and entering Venezuela, she wrote that the country would "defend its rights to free trade, navigability, free development, sovereignty and national independence."Go deeper: Why the U.S. went after Maduro