
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
A car journeys from City $X$ to City $Y$, a distance of $150$ miles, at a speed of $75$ miles per hour. It then returns to City $X$ along the same path. If the average speed of the whole round trip is $50$ miles per hour, what is the rate, in miles per hour, of the car on its return trip from $Y$ to $X$?

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