How did the hiragana and katakana syllabaries originate?

There are three traditional characters in the Japanese language:
kanji, hiragana, and katakana.
Kanji are ideograms brought from China.
We might say that kana do not convey the meaning of kanji, but rather stand for simplified sounds.
The Manyoushu, which was compiled in the mid-eighth century, contains about 4,500 waka poems; yet most are written with kanji with randomly assigned sounds.
Over time, kanji were simplified, and by the end of the ninth century, they had evolved into the current hiragana syllabary.
Katakana, which are even more simple than hiragana, developed alongside the hiragana syllabary, and was already used in written works by the beginning of the ninth century.
Hiragana came to be used in correspondence and narratives, while katakana was used for annotations and as phonetic symbols for difficult kanji.