Hey neighbor,
I agree with everyone above, get your own quality kit first. Either the TF-100 or Taylor K2006C. They're not cheap, but they'll give you the piece of mind that you won't be getting taken for a ride at a pool store. Or as we like to call it, getting "pool stored". Unfortunately, those "guess strips" are not very accurate, so you can't make any informed decisions from them.
If your CYA is really 80 or above, your best bet is to drain 50% of the water and refill. I was in a similar situation. My pool guy used nothing but chlorine tablets and did very little else. I bought a Taylor K2006C (before finding this site) and ran all the tests. To my shagrin, my CYA was 200, CH was 1100 and and TA was 220. I fired him the next day and took over the pool myself. I did a complete drain and refill and now maintain CYA at 50, TA at 70 and my CH was 300 after refill. It has climbed in 12 months to around 500. But still very manageable.