Design turn-taking for a voice agent before latency and interruptions make it feel broken

You are designing the turn-taking and interruption behavior for a real-time voice agent, before the conversational logic gets implemented against LiveKit Agents with Deepgram STT and ElevenLabs TTS. Your job is to specify exact rules for when the agent speaks, stops, and resumes — not to describe voice-agent best practices in the abstract.

CONVERSATION CONTEXT
an appointment-scheduling agent for a dental office, calm and patient tone, callers are often older and speak more slowly than average

LATENCY BUDGET
under 800ms from end-of-speech detection to the start of the agent's audio response — every rule below has to be judged against this number, since a turn-taking rule that sounds natural in a text transcript can feel broken in real time if it adds latency nobody accounted for.

TURN-TAKING RULES
- Define the silence threshold that signals the user has finished speaking — not too short, cutting off a user mid-thought who paused to think, and not too long, an awkward dead-air gap before the agent responds. State the actual number in milliseconds and what evidence supports it for this use case specifically, not a generic "a second or so."
- Define how the agent signals it's still processing when generation takes longer than the silence threshold would suggest a response is imminent — a filler phrase, a soft acknowledgment sound, or explicit silence handling. Silence with no signal is the single most common way a voice agent reads as broken, even when it's about to respond correctly.

INTERRUPTION HANDLING
- State what happens when the user starts speaking while the agent is mid-response: does the agent stop immediately, finish its current sentence and then stop, or ignore short interjections under under 400ms of user audio, and matching a short backchannel word list (mhm, yeah, right, okay) as backchanneling rather than a real interruption?
- State what the agent does with the sentence it was cut off mid-way through — silently continue if the interruption turns out to be a backchannel, discard the rest and treat it as a full turn change, or explicitly acknowledge the cutoff before deciding? Pick one and justify it against the use case — a support call and a casual voice assistant warrant different answers.

FAILURE RECOVERY
- What happens when speech-to-text returns a low-confidence or garbled transcript — does the agent ask the user to repeat themselves immediately, or attempt to respond to its best guess and let the conversation self-correct? State the confidence threshold that decides which path, tied to Deepgram's per-utterance confidence score; below 0.6 triggers a clarifying repeat-back rather than a guessed response.
- What happens on a long silence after the agent asks a question — a fixed timeout before the agent checks in, stated as a number, not "after a while."

OUTPUT FORMAT
A state-by-state description: for each conversational state — agent speaking, user speaking, both silent, ambiguous — the exact rule for what triggers a transition to another state, with every threshold as a concrete number tied to the latency budget.