
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
At 12 PM, four cars depart from point $A$ heading towards point $B$, which is $210 \mathrm{~km}$ away. The speed of the first car is the geometric mean of the sum of the speeds of the second and third cars and the speed of the fourth car. The speed of the fourth car is half the arithmetic mean of the speeds of the second and third cars. The ratio of the speeds of the first and fourth cars is equal to the ratio of the speeds of the second and third cars. Additionally, it is known that the car with the speed equal to the sum of the speeds of all four cars can travel from $A$ to $B$ in 1 hour. When do each of the cars arrive at point $B$?

Present the answer in LaTex format: \boxed{Your answer}
user