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Basil is susceptible to coldBasil is susceptible to cold conditions, and you are effectively chilling it by planting in a north-facing bed. Ditto for your tomatoes. Basil and tomatoes need full sun. Four hours is not enough; 6 (aka"part sun") is sometimes acceptable but they really need 8 hours or more, or "full sun." It's not just the "light" effect of the Sun that they need; "full sun" not only casts light but the Sun warms the soil. By watering when they can not dry out due to low sunlight/warmth, the plants are, essentially, drowning. Basil and tomatoes prefer full sun, well-draining soil, and appropriate pH. If there is any way you can plant or pot in a south-facing spot you would probably be more successful.

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