Writing to strangers is the riskiest thing for an account. That is why the outreach goes only from warmed-up accounts, slowly and with a daily limit. This way accounts live longer. Accounts that are not warmed up or are busy will be skipped.
Your offer (sent after the greeting and their answer):
Whom to write to (one @name or t.me link per line):
Each account's letters are spread evenly across your hours: e.g. two letters in a 9–21 window go about six hours apart. By our measurement 1–2 a day is safest: more than one letter per 12 hours gets every third account restricted.