
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

In the direction from $A$ to $B$, a car traveled for some time at a constant speed of $v_{1}=60$ km/h. It covered the remaining part of the way in the same amount of time, but at a speed of $v_{2}=40$ km/h. In the opposite direction, the car traveled one half of the way at a speed of $v_{3}=80$ km/h and the other half at a speed of $v_{4}=45$ km/h. What is the average speed of the trip: a) from $A$ to $B$? b) from $B$ to $A$?

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