How to increase rent on long-term tenant in CA renting ~35% below

[Kezia Edmonson]

Long story short, had a very long term lease (5yrs) on single fam home with a small (8%) increase built in already (pre-defined in original contract) in years 5-7 year.  In 6 months we're at the end of year 7, tenant wants to renew lease again BUT we are now VERY below market rate...like 35% below just the avg... How do I increase the rent significantly while navigating a long term very good tenant? 

Also, I don't think the CA rent increase rules apply since this is a single family home (it was previously my primary but moved for military), it's our only one there, and we're in San Diego county. Tenant wants to stay, I want them to stay, but they are at least $12-1500 under market now at $3450, & avg $4700-4900 in 1mi radius.

1) Does anyone have links to actual law on rent increase for my situation

2) How would you navigate this increase?  THANK YOU!