
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
Two people start walking towards each other from points M and N which are 72 miles apart. The first person walks at a constant speed of 4 miles per hour. The second person walks an increasing distance at a 2-miles-per-hour increase every hour, with distances of 2, 2.5, 3, and so on, forming an arithmetic sequence. Determine the time at which they will meet.

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