Competing deadlines
I would first confirm each deliverable's impact, true deadline, dependencies, and decision owner rather than treating both urgency labels as equal. If I could not complete both safely, I would estimate the remaining work, present the tradeoff to the person with priority authority, and notify affected partners of the approved sequence. I would document the decision and set a checkpoint before the first deadline so a new dependency could trigger reassessment. Because the scenario does not identify the organization's priority rules, I would not invent them.