
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 cyclist travels $21 \mathrm{~km}$ per hour on flat terrain, $12 \mathrm{~km}$ per hour uphill, and $30 \mathrm{~km}$ per hour downhill. The entire $80 \mathrm{~km}$ journey takes 3 hours and 55 minutes to go and 4 hours and 40 minutes to return. What are the lengths of the flat, uphill, and downhill segments of the journey on the way there?

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