Critical thinking about a topic or an issue includes the process of brainstorming and not ruling anything out too early in the process. It means thinking for one's self, rather than just accepting existing opinions and conclusions. This kind of thinking process is in contrast to rehashing memorized information. Critical thinking skills and habits are indispensable tools in the critical writing process.
Among other things, analysis entails looking at disparate things and finding patterns and relationships that are not necessarily obvious at first. With analysis, there is often an emphasis on disassembling things into separate pieces for further review.
While analysis involves taking things apart, even if only figuratively, it will eventually be necessary to reassemble these thoughts and facts. That's what synthesis does: it puts things together. If the critical thinking and analysis went well, the synthesis stage of the process will likely result in novel observations and conclusions, a fresh point of view for others to consider.
Arguments, whether verbal or in writing, can be convincing and compelling while also being untrue. A charismatic and slick politician, for example, might be able to dupe a lot of people, but a writer making good use of the critical writing tools can help reveal the truth.
It's a frustrating reality that we often reach a critical bottom line with less than complete information. The critical writer must be vigilant in these matters. In other words, the honest and effective critical writer must be critical of his or her own process and conclusions.