Multi-Step Brief Form

Build a "Multi-Step Brief Form" React component.

CONCEPT: A lead-capture brief that asks one thing at a time: project type (chips), budget (segmented), timeline (chips). A progress rail shows 3 segments.

LAYOUT & CONTENT:
- Step header: 'Step 2 of 3' mono + question in large grotesk.
- Chips: pill buttons with 1px border; selected chips fill charcoal with cream text and a check icon.
- Footer: Back (text) and Continue (charcoal pill, disabled until a choice).

INTERACTIONS & MOTION:
- Steps use AnimatePresence custom={direction}: enter from x ±60 opacity 0, exit to x ∓60, spring stiffness 320 damping 32.
- Progress segments fill cobalt with scaleX springs.
- Selected chip check icon scales in. Final step shows a summary of choices.

DESIGN SYSTEM (non-negotiable):
- Palette: paper background #FAF9F6, deep charcoal #121212 for text and 1px borders, ONE warm accent: cobalt #1D4ED8 or terracotta #D9534F. Secondary surface #F2EFE8.
- Typography: Swiss / editorial. A tight grotesk for UI (Instrument Sans, Inter Tight or similar) with negative tracking on display sizes; an italic serif (Instrument Serif) used sparingly for one emphasized word.
- NO dark-mode neon, NO glow, NO glassmorphism, NO backdrop blur, NO purple-to-blue gradients, NO emoji icons. Solid fills, hairline rules, honest shadows (hard offset or none).
- Motion: Framer Motion with spring physics (type: "spring", stiffness 300-500, damping 20-35). Animate transform and opacity only. Respect prefers-reduced-motion via useReducedMotion().
- Icons: lucide-react, 1.5px stroke.
- Accessibility: real <button>/<a>/<label> elements, visible focus ring (2px cobalt, 3px offset), keyboard operable, aria attributes where state changes.

OUTPUT: one self-contained React component file (Tailwind CSS v4 utility classes, framer-motion, lucide-react), no external images, default export, ready to paste into a Next.js App Router page with "use client".