Question: What actor who began her acting career at a young age, and quickly became labeled a teen idol as the title character of the Disney Channel comedy series "Lizzie McGuire", wrote a song for her first compilation album with the Dead Executives?

<P0-S0> "Wake Up" is a song recorded by American singer Hilary Duff for her first compilation album, "Most Wanted" (2005). <P0-S1>  It was co-written by Duff and the Dead Executives, who also produced the song. <P0-S2>  Along with the three other new recordings on "Most Wanted", "Wake Up" was crafted with the intention of having a "totally different sound" from Duff's previous material. <P0-S3>  Although she thought of the work to be a new milestone in her career, she was at the same time nervous about her fans would react to the material. <P0-S4>  "Wake Up" was released as the lead single from "Most Wanted" on July 12, 2005. <SEP> <P1-S0> "Beat of My Heart" is a song recorded by American singer Hilary Duff for her first compilation album, "Most Wanted" (2005). <P1-S1>  It was written by Duff and the Dead Executives, a record production team consisting of Jason Epperson, Joel and Benji Madden. <P1-S2>  Along with the three other new songs on "Most Wanted", "Beat of My Heart" was crafted with the intention of having a "totally different sound" from Duff's previous material. <P1-S3>  It is an up-tempo new wave-inspired electropop song that incorporates elements of bubblegum pop and dance music in its production. <P1-S4>  Lyrically, "Beat of My Heart" can be interpreted in many different ways. <P1-S5>  For Duff, it tells the story of a woman "com[ing] out of her shell again" after a bad break-up. <SEP> <P2-S0> “Why Not” is a song recorded by American actress and singer Hilary Duff for the soundtrack of the 2003 comedy film, "The Lizzie McGuire Movie," which was produced and released at the time when Duff was starring as the title character of the Disney comedy series "Lizzie McGuire." <P2-S1>  Its lyrics were written and its music was composed by Charlie Midnight, who collaborated on both with the song's music producer, Matthew Gerrard. <SEP> <P3-S0>  Duff began her acting career at a young age, and quickly became labeled a teen idol as the title character of the Disney Channel comedy series "Lizzie McGuire" (2001–2004). <P3-S1>  The series proved to be a hit, leading to a film adaptation of the series to be released. <P3-S2>  Duff began working on numerous projects with the Disney Channel, including the film "Cadet Kelly" (2002). <P3-S3>  She later began work on an album, releasing the Christmas themed "Santa Claus Lane" (2002) through Walt Disney Records. <P3-S4>  Upon signing with Hollywood Records, Duff began working on her second studio album, "Metamorphosis" (2003). <P3-S5>  The album achieved critical and commercial success, topping the U.S. "Billboard" 200 and selling over three million copies in the nation. <P3-S6> Hilary Erhard Duff (born September 28, 1987) is an American actress and singer. <P3-S7>  It also found success in both Canada and Japan. <P3-S8>  Duff's success in both acting and music led to her becoming a household name, with merchandise such as dolls, clothing, and fragrances being released.