A number of people have speculated on the next moves for Russia. Here I would like to take a stab at this.
Before I speculate, let's assign the goals of the Russian war against Ukraine. The War on Ukraine is a Russian counter-attack after NATO crossed one too many redlines with no regard for Russian interests and security concerns. NATO didn't have to expand all the way to Ukraine. Out of past momentum and inattentiveness, NATO assume incorrectly that Russia would not dare to attack Ukraine. This war, Russia must defeat NATO in the country that used to be Ukraine.
To defeat NATO, Russia must
1. Change the perception and the psyche of all Ukrainians, pro or against Russia. They must accept that no one, including NATO, however hard they have tried, can save them from Russian arm forces. This can only happen if Ukraine is defeated decisively after a prolong war with Russia, notwithstanding all the help that NATO has or will send. This change of psyche will turn the Ukrainians against those who caused them to go to war in the first place. It will turn them against NATO and the current Ukrainian government.
2. Change the perception and the psyche of other Eastern European countries like Lithuania so that they too, realize that NATO cannot stop the Russians from taking over their country. This will happen after Russia successfully conquer Ukraine.
3. Conquer and incorporate regions that are pro-Russia or indifferent.
4. Conquer and destroy regions that are anti-Russia.
5. Corollary to 4. above, drive out as many Ukrainians that are anti-Russia and send them packing to the West. repopulate Ukraine with more pro-Russian Ukrainians
A few side benefits that may follow and is nice to have,
6. Change the European government to a less anti-Russian one.
7. Weaken the Western European countries so Eastern Europe is more isolated and must fend for themselves.
8. Since relationship is soured with Europe, it would allow Putin a freer hand to re-orient the Russian economy towards the East.
So here is what I expect
Phase2, Conquering Donbass. This is ongoing. It will be completed when Kramatorsk grouping is destroyed.
Phase3, Southern Big Cities, straighten out the frontline as much as possible and slowly push towards multiple cities, Kharkiv, Zaporizhzhia, Mykolaiv. Let the Ukrainians bring their troops all the way across the country to fight the Russian army that is near the supply line and have a straight frontline. Once one of these cities buckle, send in the reserve force to attack it and conquer.
Phase4, Southwest Ukraine, Once all the cities in Phase3 is done, push north in a single broad front, avoid but surround Odesa, and push Northward from both sides of the Dnipro river, taking cities like Dnipro and Kremenchuk along the way.
Phase5, Zumy and rest of Eastern Ukraine
Phase6, Kiev
Phase7. Northwest Ukraine, Send an expeditionary force to fight and destroy what remains of Northwestern Ukraine, do not conquer it, and encourage all the anti-Russian Ukrainians to go there. Do not declare ceasefire and wait until most of these move on to Poland and beyond. Since no industry is possible after everything is broken, most will choose to move away once they arrive here from other parts of Ukraine. The Russians can either keep this as a buffer, or if they feel that NATO is still trying to come into this region, conquer it once it is de-populated.