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You could work with applications also offline, when you don't have a good Internet connection. You can choose and install an operating system, such as Windows, Ubuntu Linux, Mint, other Linuxes, and the version you like. With a normal Laptop, you have the power over it. There were MonkeyTeX and Spandex.io, both gone now. And it happened several times, that LaTeX cloud services were closed and vanished. I know them as pretty slow, often, I'm impatient when writing and compiling. Commercial things require money directly or indirectly (such as by advertisement). However, you need to pay for full features.
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There are a very few LaTeX online services, most capable are Overleaf and ShareLaTeX. With a Chromebook, you are bound to google and the google app store, you should always have an internet connection for working in the cloud, which also means you are restricted to cloud services.
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