
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
William is biking from his home to his school and back, using the same route. When he travels to school, there is an initial  $20^\circ$  incline for  $0.5$  kilometers, a flat area for  $2$  kilometers, and a  $20^\circ$  decline for  $1$  kilometer. If William travels at  $8$  kilometers per hour during uphill  $20^\circ$  sections,  $16$  kilometers per hours during flat sections, and  $20$  kilometers per hour during downhill  $20^\circ$  sections, find the closest integer to the number of minutes it take William to get to school and back.

*Proposed by William Yue*

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