Lovable prompt for a 404 page

Add a custom 404 screen to my a project management SaaS app — a single viewport-height page that turns a dead end into a recovery moment for engineering managers at startups. Register it as the catch-all route so any unknown URL lands here, and make sure it responds with an actual 404 status.

Compose it as a split layout:
- Left, 60% width: a short stack — small a project management SaaS wordmark, an error headline written in the product's voice (playful but useful, hinting at what the visitor was probably looking for), one supporting sentence, then two recovery paths: the primary button and a text link that goes back to the previous page via history.
- Right, 40% width: a decorative panel that visualizes "lost" in a way that fits the brand — an abstract composition using the palette's accent tones, never clip art.

Below the buttons, add a compact "Were you looking for one of these?" list: the four most useful pages, each with a one-line description.

Make the page earn its keep: log every 404 hit to a broken_links table (path, referrer, timestamp) using the built-in database, and include a one-field "Report this link" form that flags the matching row when submitted, swapping to an inline thank-you state.

Visual direction:
Minimal dark style. Near-black canvas (#0A0A0B) with one elevated surface tone (#141416) for cards — never more than two surface steps. Hairline borders (1px, white at 8% opacity) instead of shadows; if a shadow is unavoidable use 0 1px 2px rgba(0,0,0,0.4) and nothing softer. Text in exactly three steps: white at 92% for headings, 60% for body, 40% for captions. Generous negative space — section padding at least 120px on desktop, 64px on mobile. The accent color appears only on interactive elements and one hero highlight, nowhere else.

Palette: a strict neutral ramp (white, #F5F5F5, #E5E5E5, #737373, #171717) carries the entire interface; pick one accent and use it only for primary CTAs, active states, and a single hero highlight. If the accent appears more than five times per viewport it stops being an accent. Keep semantic colors (success, error) desaturated so the accent stays in charge.
Typography: one geometric sans (a Futura/Poppins-class face) at three weights maximum (400/500/700). Scale: 64-88px hero, 32px section heads, 18px lede, 16px body, 13px caps labels with 0.08em tracking. Tight headline leading (1.05-1.1), relaxed body (1.6). Let the geometry carry the personality — no italics; weight and size do all hierarchy.
Motion: none. Zero scroll animations, zero entrance effects — the page is fully composed the instant it paints. Spend the motion budget on input feedback instead: 120-150ms ease-out color and transform transitions on hover and press states only. Hold this constraint absolutely; it is a statement, not an omission.

Rules:
- The whole page fits 100vh on desktop; internal spacing uses 12/20/32px steps, and no gap between siblings exceeds 32px.
- On mobile, the decorative panel shrinks to a slim banner above the text stack and the page may scroll naturally.

The primary call to action is "start a free trial" on the main recovery button.

After building, confirm: visiting a garbage URL renders this page with a 404 status; a row appears in broken_links with the correct path; submitting the report form flags that row and shows the thank-you state; the desktop layout fits 1280x800 without scrolling.