You are working with scikit-learn model selection tools to evaluate and compare models in a consistent way.

1. Split the dataset X and y into training and test sets using train_test_split with:
   • test_size=0.25;
   • random_state=42.
2. Create a LogisticRegression estimator with max_iter=1000.
3. Evaluate the estimator using cross_val_score with cv=3.
4. Create a GridSearchCV object named grid_search with:
   • the estimator;
   • the parameter grid param_grid;
   • cv=3.
5. Fit grid_search on the training data.
6. Store:
   • the mean cross-validation score in cv_mean_score;
   • the best parameter dictionary in best_params.