We’ve found a live test bug in the appointment flow.

Context
- Conversation is already in an appointment flow:
  - LIA has sent APPOINTMENT_TIME_CHOICES with two slots (e.g. “10:00am or 2:00pm”).
  - appointment_status is INVITED.
- From my phone, I then reply: “Can we do 11?” (or “11 would be good”).

What I see in Make (HTTP2 → /api/lia/inbound):
- Status: 200
- JSON body shows:
  - conversation_id: 9a1c02d3-1b2f-4525-b004-866e493ccbd4
  - mode: AWAITING_MANAGER
  - status: active
  - defer_until: null
  - reply: ""   (empty)
  - stage: "12"

Because reply is empty, my Twilio module correctly does nothing – but the behaviour is wrong. LIA should be confirming the appointment, not escalating.

Expected behaviour
- When the customer is already in a slot-offer flow and replies with a clear time like:
  - "Can we do 11?"
  - "11 works for me"
  - "11 would be good"
- AND last_reply_type was APPOINTMENT_TIME_CHOICES for this conversation:
  - Mode should be APPOINTMENT_CONFIRMED (or equivalent)
  - appointment_status should move to BOOKED
  - needs_human_review should be cleared
  - reply should be a confirmation message, e.g.:
    "No problem – I’ve booked you in for Saturday at 11:00am at Lincoln Audi. If anything changes, just drop me a message here and I can move it for you."

What I think is happening
- The current time detection only picks up patterns like:
  - "11am", "11:00am", "11 o’clock", "2pm", etc.
- It probably doesn’t treat plain “11” (without am/pm) as a valid time, even when:
  - last_reply_type == APPOINTMENT_TIME_CHOICES
  - pending_slot_options and/or pending_day_display are present
  - appointment_status == INVITED

Request – concrete changes
1) In the URE, update the appointment confirmation logic so that:
   - If:
     - last_reply_type == "APPOINTMENT_TIME_CHOICES"
     - AND we’re in an INVITED / APPOINTMENT flow
     - AND the latest customer message contains a number that plausibly refers to one of the offered slots (e.g. “11”, “11 please”, “can we do 11?”)
   - THEN:
     - Treat it as a time selection even without explicit “am/pm”
     - Derive a sensible default time from the context (e.g. map “11” → “11:00am” when the offered slots included 10:00am and 2:00pm)
     - Set mode = APPOINTMENT_CONFIRMED
     - Set appointment_status = BOOKED
     - Clear needs_human_review (if previously set)

2) Add tests similar to:
   - Existing flow:
     - Customer: “Can I come Saturday?”
     - LIA: offers slots (APPOINTMENT_TIME_CHOICES)
     - Customer: “Can we do 11?”
       → Expect APPOINTMENT_CONFIRMED + confirmation reply (with day + time + Lincoln Audi)
   - Variants:
     - “11 would be good”
     - “11 works for me 👍”

3) Keep the existing guards:
   - Cold inbound “Are you open at 11?” with no appointment context must still **NOT** auto-book.
   - Only auto-confirm when:
     - We’re in an appointment flow
     - last_reply_type reflects slot offering
     - The message is clearly a reply to those slot options.

Once that’s patched, I’ll retest from my phone with:
- “Can I come Saturday?”
- LIA offers slots
- “Can we do 11?”
and confirm I see APPOINTMENT_CONFIRMED and a clear confirmation message.