How is the quote, "Community. Identity. Stability" achieved within the World State? Explain by providing quotes from the text.

In Aldous Huxley's Brave New World, those in power have engineered a society that is community-oriented and impeccably stable. People's identities are assigned to them at birth, and this creates a communal identity of harmony and stability.
The first two words in this quote are connected. In this society, people are taught that the only identity they should have is a communal identity. A popular hypnopedic teaching asserts that

Everyone belongs to everyone else.

People in the World State are discouraged from thinking that they are individuals who belong to themselves. No one can act in their own interests. Instead, they must always do what is best for the community. Another hypnopedic teaching states:

When the individual feels, the community reels.

Citizens are hindered from experiencing deep emotions. Their entire lives are filled with distractions to prevent them from engaging any profound ideas. This is why Helmholtz does not find belonging and is ultimately rejected by this community. He is an intelligent thinker who considers himself an individual and experiences deep emotions.
Stability is the greatest concern of those who control the World State. In order to create a world of stability, any inconveniences or misfortunes are removed. People are prevented from developing serious relationships or experiencing fear and sadness. Mustapha Mond explains:

The world's stable now. People are happy; they get what they want, and they never want what they can't get. They're well off; they're safe; they're never ill; they're not afraid of death; they're blissfully ignorant of passion and old age; they're plagued with no mothers or fathers; they've got no wives, or children, or lovers to feel strongly about; they're so conditioned that they practically can't help behaving as they ought to behave.

This stability is engineered at the cost of romance, high art, love, sadness, familial relationships, and self-awareness. There is no purpose to life other than entertainment and consumption. This is how community, identity, and stability are achieved in Brave New World.