= Solution
Use separate <randomization> lists for women with and without a self-reported history of depression. Within each <stratum>, the central service could assign intervention and control in a $1:1$ ratio using randomly permuted blocks, preferably with concealed and varying block sizes. This is <stratified randomization>; the internet service can retain <allocation concealment> because the recruiting staff do not know the next assignment.
History is plausibly prognostic for the outcome. Keeping its distribution similar between arms reduces the risk of a chance imbalance in that important baseline factor and can improve precision. It also allows a comparison within each history <stratum>. Stratification does not guarantee balance of every other <covariate>, and staff must not be allowed to choose assignments. The <regression model> can retain history as a <baseline covariate>, respecting the design.
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