Sync Project Task Matrix and Recalculate Milestones

You manage a project tracking database where each project contains an array of milestones, and each milestone contains an embedded array of tasks. You need to perform a complex maintenance operation across all active projects. First, for every project where the status is 'in_progress', find all milestones that have an array of tasks containing at least one task marked with priority: 'high' and completed: false. For each of these matching milestones, push a new warning task into its tasks array with the title: 'Audit Required', priority: 'urgent', and completed: false, but only if a task with that exact title does not already exist in that milestone's tasks array. Second, update the project level last_audit_date to the fixed ISODate('2024-06-01T00:00:00Z') for all affected projects.### Collections#### projects - _id: Integer - name: String - status: String ('in_progress', 'completed', 'archived') - last_audit_date: Date or null - milestones: Array of embedded documents containing: - milestone_id: Integer - title: String - tasks: Array of embedded documents containing: - task_id: Integer - title: String - priority: String ('low', 'medium', 'high', 'urgent') - completed: Boolean### TaskExecute a single or multi-stage update operation on the projects collection using updateMany that targets projects with status: 'in_progress', adds the audit task to the relevant milestones using array update operators and positional operators without duplication, and sets last_audit_date.### ExampleOn the visible dataset, running this update will modify projects that have in_progress status and meet the task criteria.