Do Not Use the Google Framework Services "Trick"
If you start getting impatient, look into the manual installation process. Do not use the Google Framework Services "trick."
For many years, the Google Framework Services "trick" was promoted as a way to force an OTA update. While it might work, it has the potential to harm your device. As a reminder, here's what a Google engineer had to say about it:
"Doing this changes the primary ID by which Google knows your device. As far as the servers are concerned, the device was basically factory reset. There are many downstream effects of this, but a big one is that this invalidates the tokens used by any app that uses GCM (which is nearly all the Google apps, and a ton of third-party apps.)
How apps react to GCM IDs changing varies by app. With Play Store you have to log out and log back in, I think Gmail usually handles it transparently eventually but won’t get new mail notifications for a while, etc. Some apps you may have to clear data on to recover. All apps will simply stop getting GCM push-messages, until they get a new GCM ID; some do this frequently, others rarely, and some apps use the GCM ID as an ID on their own servers (as it is opaque and basically random), so other things besides push messages may not work.
Nothing bursts into flames, but it makes a ton of nuisances on the device, including some that can look pretty mysterious. Your mileage will vary depending on what apps you use."
If that's not convincing enough, take a look at what Google itself has to say about this "trick." Don't use it. Sideload or wait for the OTA.
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