
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 carts are racing down two parallel hills. The first cart travels $6$ inches in the first second and accelerates so that each successive $1$-second time interval, it travels $8$ inches more than during the previous $1$-second interval. It takes $35$ seconds to reach the bottom of the hill. The second cart starts $2$ seconds after the first and travels $7$ inches in the first second, then each successive $1$-second time interval, it travels $9$ inches more than the previous interval. Find the distance, in inches, the second cart travels by the time the first cart reaches the bottom of the hill.

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