"continue on their path" is a correct and usable phrase in written English.
It means to continue moving forward or following a specific direction or course of action. You can use it to describe someone or something continuing their journey or progress, either physically or metaphorically. Example: After facing numerous obstacles, the team decided to continue on their path towards success and eventually achieved their goal.
Assuming the Knicks — who have not made the playoffs since 2004 — continue on their path, the Jazz could claim a high lottery pick in 2010.
Mr. Paul's amendment would have created a series of stricter border security requirements and required Congress to vote every year for five years that it believed the border was secure, before immigrants could continue on their path to legalization.
Also present was Aleksandar Vucic, the Serbian deputy prime minister, a former extreme nationalist.The agreement unlocks the way for both countries to continue on their path to EU integration.
The date by which Halliburton and Baker Hughes would have to decide whether to continue on their path of regulatory approval or terminate their merger agreement was extended to April 30.
Pope Francis was seen as playing a key role in the re-establishment of diplomatic relations between Cuba and the US, and he used his first speech in Havana on Saturday to urge leaders from both countries to continue on their path to reconciliation.
UN Secretary General Ban Ki-moon's special adviser for Yemen, Jamal Benomar, meanwhile stressed that "such criminal acts seeking to terrorise Yemenis will only strengthen their resolve to continue on their path of peaceful change".
If we truly want countries like Ghana to continue on their paths of progress, and the poorest countries to catch up, we need a new vision for what aid should do.
Then, after seeing Brady and the Patriots expose the Steelers, the Raiders continued on their path.
The course of events that had precipitated the January 25 revolution continued on their path, spewing lava as the revolution unfolded.
Never mind that in the days after the attack, Tsarnaev and his older brother, Tamerlan, held the people of Boston hostage and continued on their path of destruction, which included a carjacking and the death of a MIT officer.
For the following century the two materials remained in intense competition, both offering a similar product at a similar cost, and there was little evidence that one would move far ahead of the other as they continued on their paths of gradual improvement.
