Well, as bad as it sounds, you might need to consider that your Players don't want to play High Level PC's. This isn't a slam against them, or you, it is a possible reality.
Playing a high level PC means you have to be well-versed in your abilities. Especially spellcasters! It does require that the players devote more energy to learning the ins and outs of the PC. If your players are unable/unwilling to devote this type of energy to the PC, then they will not be able to use the full set of options high level PCs have. It is unfortunate, but that sometimes happens.
Of course the issue could also be exactly what you are speaking of: the players have the will, but are lacking the direction. In this case, rejoice. The situation can be managed and improved.
First of all, when you find the group bogged down and locked in a train of thought, consider taking a break. Grab some dinner, watch some anime, take a smoke break, whatever. Sometimes you just need to step back and take the pressure off for a little bit.
Second of all, find a way to give them a solid butt whooping and then leave the conclusion for the next session. Impending death with a week to think about it sometimes provides quite an impetus to think creatively. Be warned, this is a risky tactic and with some groups could backfire immensely.
Thirdly, demonstrate some of the tactics you are looking for the PC's to adopt. I would avoid the chastisement. Instead, have a friendly NPC request an assist. Perhaps somebody just made the wrong enemy and they are buffing up the defenses on their sanctum. Trusting the PC's, the NPC asks for some temporary bodyguard work while defenses are being prepared. Or the PC's might be asked to help go on the offensive. Maybe they are asked to help with the buff portion of a friendly groups scry-buff-teleport plan. Or even contribute to the assault. Perhaps a lower level NPC asks for help with a scry to find his runaway daughter? Since the PCs are so powerful and compassionate, he was hoping they would be able and willing to help him? There are many possibilities where the PCs can have the tactics pointed out without it being a degrading experience.
Provide a challenge that can only be solved with more powerful magic. When one of my groups was moving into the higher level zone, I gave them a challenge that would be simple for higher level casters to solve. I setup a passageway that ended at a chasm. The Chasm was 40 or 60 feet across. They couldn't see the top and they couldn't see the bottom. The passageway continued on the other side, a good 20 feet to the right. The PCs debated this for quite a while. The passageway was situated where a jump wasn't feasible. Throwing a rope across wasn't feasible. Climbing was impractical except for very skilled characters. The group thought of several mundane solutions. They tried to disbelieve illusions. the looked for the secret panel that would make a bridge, etc. They couldn't believe there was no way to get across. Then with a shrug, the party wizard suggested that he just make a bridge with his wall of stone. Then they could pass back and forth at will. After they discussed it a little longer and came up with many solutions that demanded high level PCs, they began to "get it". The place they were at was a challenge that was not meant to be easy. You had to be good to get past all the challenges in that place. Later on, one of the players asked me how they were "supposed" to get across. I told the player that only power characters could get across. Which brings me to my last suggestion.
You might just sit down after the session and toss out some what-if scenarios and point out that the players are selling themselves short. Explain that the reason high levels are fun is that the PCs have so many options. As a DM, you worry less about "the solution" because the PCs will have many possible solutions. You provide a challenge and then watch with amazement at how effectively the players deal with those challenges. Then point out that you aren't dealing with Orcs in dungeons. The PCs can change the world. As players, they just need to get used to having that many options and then they need to just have fun. Of course, this only works if you are able to avoid all problems only having one solution and if you truly allow the PCs to change the world. But it is a growing experience for all the players, including the DM. So perhaps your best option is to simply be honest and communicate with the players.
I'm not sure which of these answers, if any, will help. But I hope one or more of them does. High level play is a lot of fun.