
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 cart rolls down two sections of a hill. For the first 15 seconds, it travels 8 inches in the first second, with each successive 1-second time interval seeing it travel 10 inches more than during the previous interval. After 15 seconds, it hits a smoother section of the hill, where it starts with the speed it had at the end of the first 15 seconds and decreases its acceleration such that it only gains an additional 6 inches each second for another 15 seconds. Calculate the total distance traveled by the cart in these 30 seconds.

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