
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 travels the 150 miles from $A$ to $B$ at 75 miles per hour, and then returns to $A$ on the same road. The car also takes a 30-minute break during the return journey. If the average rate of the round trip is 50 miles per hour, what is the rate, in miles per hour, of the car traveling back from $B$ to $A$?

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