A NEW SONG: Singer/songwriter Natasha Bedingfield and Coty Inc. are teaming up to give hope to those with mental illness. Bedingfield — along with a writing and production team made up of Matt Robinson, David Saw and Ryan Freeman — penned a song for Coty Inc.’s Philosophy brand to celebrate the release of its new Renewed Hope in a Jar product. The song, priced at $1.29, became available for download on Tuesday on iTunes, with 20 percent of the net proceeds to benefit Philosophy’s Hope and Grace foundation until 2016. The foundation, founded in July 2014, supports community-based mental health organizations. Bedingfield will do the first live performance of the song at a Coty party on Jan. 20. The performance will be simulcast via Livestream as part of a larger digital media campaign that will further promote the Renewed Hope in a Jar product and the Hope and Grace initiative.