Examples in the story:
- Past Simple: 'cycled', 'began', 'began', 'swam', 'had', 'said', 'left', 'invited', 'smiled', 'said', 'had', 'feeling', 'tired', 'left'.
- Past Continuous: 'was shining', 'was walking', 'started', 'was beating', 'walked', 'called'.
- Used to: 'used to love swimming'.
- Modal Verbs (speculation/deduction): 'might have forgotten', 'can't have left', 'might be shy'.
Answer: The examples of different past tenses and modal verbs are listed above.