The following page of the game guide to Marvel's Spider-Man contains the descriptions of the missions titled respectively "The Mask" and "A Day to Remember". These short tasks require you to return to the F.E.A.S.T. headquarters, talk to Martin Li and visit Dr. Otto.
Before starting the missions, you should definitely consider completing any side quests and activities that are available to you at this point in the game. The discussed task is really a prelude to much more demanding missions - make sure you choose the correct Spider-Man suit for the occasion and upgrade your gadgets.
Meanwhile, however, you should head to the F.E.A.S.T. headquarters. Peter will wait out the night and enter the facility in the morning. As before, you can interact with the different people and objects here. If you are looking for some additional fluff in the game, search this location thoroughly. In the picture above you can see Uncle Ben's clothes collection.
When you are ready, go upstairs and enter Martin Li's office. Peter will ask the man for the origin of the mask, which he found during the visit to the museum. The man's attitude will begin to raise some concerns about his true intentions...
After all of the above has been done, leave the location, and this short mission will come to an end - you will gain 1500 XP.
A Day to Remember
You must go back to Octavius's ??laboratory. A cutscene will await you there, in which you will see that the doctor has lost all of his funding. After this revelation, the mission will end - the game will reward you with 250 XP.