Plan simple cuts without counting the same scrap twice

Use the complete sample brief below to make one feasible coordinate layout. Return the complete requested result, including all pieces, a non-overlapping partition of offcuts and area checks. Explain the coordinate origin. Use the stated zero-width-line assumption only for this exercise. Do not claim an optimal plan, physical cutting or an actual tool test.

SAMPLE INPUT
SYNTHETIC PAPER LAYOUT BRIEF
One rectangular paper sheet: 210 mm wide × 297 mm high.
Leave a 5 mm margin on every outside edge. Coordinates start at the sheet's upper-left corner; x increases rightward and y increases downward.
Need six separate rectangles, each 60 mm wide × 80 mm high. Rotation is permitted, but this sample uses all six unrotated.
For this sample, place the six unrotated pieces tightly together in two columns by three rows, anchored at (5,5). The right offcut must stop at the bottom of that piece block; use one full-width bottom offcut beneath it. These sample-only arrangement rules make the worked-example checks specific; they are not a claim that other layouts are impossible.
For this planning exercise only, pencil layout lines have zero width and no material is lost between neighboring rectangles. No real blade width, cutting allowance, equipment or physical cut is modeled. If planning a real cut, obtain its actual allowance and safe method before using any layout.

REQUIRED RESULT
Give one feasible coordinate plan, not a claim of the best possible packing. List every requested piece once with x, y, width and height in mm. Partition all remaining usable space into non-overlapping rectangular offcuts and list those too. Do not count the same scrap in two offcuts or treat the outside margins as usable offcuts. Reconcile piece area + offcut area = usable area, and usable area + margins = sheet area. Keep a digital coordinate proposal separate from a measured physical result. Do not operate tools or provide cutting-machine instructions.

Audit the full coordinate table against the original sample brief in this chat. Check every requested piece exactly once, inside margins, orientation, pairwise interior overlap and leftover coverage. Recalculate piece, offcut, usable and total sheet areas. In particular, ensure no bottom-right scrap is counted twice. If a row fails, give a corrected complete table and all area checks. Keep physical fit and cutting unperformed.

Make one feasible rectangular material layout from MY INPUT. List each requested piece exactly once, with ID, x, y, width, height and rotation. Respect all margins and allowances. Partition the remaining usable material into non-overlapping regions; if rectangular offcuts are not sufficient, describe the remaining geometry explicitly rather than double-counting it. Give traceable area totals and separate material loss from reusable offcuts. Do not claim optimality or physical fit.

MY INPUT
Sheet dimensions and units: [replace]
Piece IDs, dimensions and quantities: [replace]
Allowed rotations and material direction: [replace]
Outside margins: [replace]
Actual cutting allowance and how it is applied: [replace, or state unknown and block physical use]
Coordinate origin/directions: [replace]
Other exclusions and human safety boundary: [replace]

Use these values, not the sample sizes or counts. Ask for missing essential dimensions or contradictory rules before completing the plan. Check all boundaries and pairwise overlaps, then account for every region once. Return the finished proposal plus a human measurement/check list. Do not operate tools, generate machine-control code, cut or overwrite the source measurements. If an allowance is unverified, say exactly what remains unresolved.