Before he became President of the United States, Donald Trump’s catchcry on The Apprentice was “You’re fired!”. Now that he is the leader of the Free World it’s not so easy: he needs others to hand out the termination notices.

Terminating Bashar al-Assad in Syria and North Korea’s Kim Jong-un in particular – but seeing the end of either one or both those dictators –depends on winning the cooperation of Russia and China.

Winning that cooperation will be US Secretary of State Rex Tillerson’s brief when he touches down in Moscow after his whistle-stop visit with the leaders of the G7 nations in Italy on Tuesday.

Even without last week’s US cruise missile blitz on the Syrian airbase that mounted the horrific poison gas attack on the rebel-held city of Khan Sheikhou, Mr Tillerson’s job would have daunting.

The US suspects the Kremlin of arms-control violations and has criticised what the Trump administration sees as a lack of genuine effort  to defeat Islamic State.

In Washington the thinking goes that Russian President Vladimir Putin is more interested in propping up President Assad than defeating Islamic extremists.

Now, on top of that, there is the fallout from last week’s US attack, with the early indications being that the Russians are in no mood to play nice.

Where a visiting Secretary of State could normally expect an audience with the Russian President, the Kremlin has let it be known that there are “no plans” for talks with Vladimir Putin.

Instead, unless Mr Putin has a change of heart, Mr Tillerson will only meet his direct counterpart, Foreign Minister Sergei Lavrov.

Still, analysts see the possibility of Russia making some concessions, especially with British PM Theresa May and other world leaders calling on Mr Putin to renounce Mr Assad – something he might, just might, be prepared to do, according to respected Australian analyst David Kilcullen.

“Syrians I have spoken with aren’t loyal to Assad the man – he can go, but they point out that some elements of the regime must remain in place or there will be chaos,” he said.

“The Russians don’t want to restore Syria to the way it was, that’s not their priority, which is safeguarding their naval bases on the Syrian coast and maintaining a buffer zone to keep them secure.”

Moscow could live with that, Mr Kilcullen said.

Mr Assad still controls about a third of Syria, Mr Kilcullen told Melbourne radio station 3AW. Mr Putin might consider placing a new puppet in Damascus, the Syrian capital, as Mr Assad becomes more of a liability to Moscow than an asset, he said.

That would make everyone happy: Mr Trump could boast that Mr Assad had been driven from power while Russia would keep its bases. It would also give war-weary rebel factions an opportunity to negotiate with Mr Assad’s’s theoretical successor while also creating the potential for a stepped-up campaign against ISIS.

On the other side of the world the signs are both positive and contradictory.

After Chinese president Xi Jinping’s weekend visit to Mr Trump’s Mar-a-Lago estate, Mr Tillerson said that Washington and Beijing agree that Kim Jong-un needs to be reined in or thrown out.

“President Xi clearly understands, and I think agrees, that the situation has intensified and has reached a certain level of threat that action has to be taken,” Mr Tillerson said.

This was followed on Monday by reports that China and South Korea  have formulated a list of tough sanctions on North Korea if the country carries out further missile tests, according to an official in Seoul.

Yet even as Mr Tillerson expressed optimism, China on Tuesday announced that it had rushed 150,000 troops to the North Korean border in what was widely seen as a reaction to the possibility that Mr Trump would unleash another barrage of missiles.