
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
Alice drives to work every weekday, setting off at the same time each morning. If she drives at an average speed of 45 miles per hour, she arrives 5 minutes early, and if she drives at 65 miles per hour, she arrives 7 minutes early. Calculate the speed at which Alice must drive to arrive at work exactly on time.

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