
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 circular running track is split into two segments: the first half-track has concentric circles whose circumferences differ by $20\pi$ feet, while the second half-track's concentric circles differ by $30\pi$ feet. If the total track width varies linearly from one segment to the other, and the average width of the track is required, what is the average track width in feet?

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