So this is my problem, spell caster with a bow.

Round 1

1. Equip bow as free object interaction (PHB.190)
2. draw and load ammunition as part of ammunition property (PHB.146)
3. attack
4. end of round 1

Round 2

1. Release one hand from the bow ([Not an action](http://www.sageadvice.eu/2015/04/12/dropping-weapons/) )
2. Draw spell focus as a free object interaction
3. cast a spell preforming its eventual somatic component with the same hand as the focus (Source: 5e System Reference document p.102)
4. end of round 2

Round 3 (here the problem starts)

1. Sheathe spell focus as a free object interaction (could probably drop it but would rather not)
2. RAW I would need to use a free object interaction to equip the bow two-handed again. but again according to [this](http://www.sageadvice.eu/2015/04/12/dropping-weapons/) the intent is manipulating objects or picking objects up. All my character does is move his hand
3. draw and load ammunition as part of ammunition property (this is also a part that requires the character let go of one hand of the bow to get the ammunition)
4. attack
5. end of round 3

What are your thoughts on this does the rule RAW or RAI (from credited sources) support this?