「~しながら」はいくつかの言い方があります。
まず, to XX and XX / to XX and XX at the same time
テレビを見る + 部屋を掃除する
例文: I watched TV and cleaned my room at the same time.
次, to XX while XX-ing
例文: I watched TV while cleaning my room.
最後に, to XX as I XX
例文: I watched TV as I cleaned my room.
泣く - to cry
〜〜ながら - whilst 〜〜
泣きながら - whilst crying
頼む - to ask, to beg, to plead, to request
泣く時 beg と plead が1番いい
Cried and pleaded
Cried and begged
Begged whilst crying