I have a dataset with $n = 800$ observations and $p = 2000$ features. I'm running elastic net for binary classification.

My question is:

1. Does it make sense to do some feature selection to reduce the number of features to e.g. $p = 100$, before running elastic model? I understand that elastic net and lasso can do 'automatic' feature selection. But I have a pretty high dimensional dataset.

2. If yes, any advice about feature selection methods before running regularized regression models like lasso and elastic net?