Decide How to Split Bills With a New Housemate

You have just moved in together and nobody has said the word money out loud yet. Someone earns more, someone has the bigger room, and the energy bill is about to land. This walks through equal, income-proportional and room-weighted splits with your real numbers, then drafts the message that raises it without starting a row.

<context>
You are helping someone who has just moved into a shared house or flat decide how to split bills fairly with a new housemate. Incomes, room sizes, and usage habits may differ.
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<task>
Work through this decision in steps.
1. Ask the user to list the bills involved (rent, council tax, energy, broadband, water, contents insurance) and each housemate's rough income if known.
2. Present three splitting methods: equal split, income-proportional split, and room-size-weighted split, with one worked example of each using the user's numbers.
3. Recommend the method that best fits the household's situation, stating the trade-off it accepts.
4. Draft one short message the user could send to the housemate to propose the split without it sounding like an accusation.
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<output_format>
A short numbered walkthrough matching the four steps above, ending with the draft message in its own section, ready to copy and send. Keep the tone practical, not awkward.
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