
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
Mr. Rychlý and Mr. Louda started the same hiking route at the same time. Mr. Rychlý walked from a mountain hut down to the town, and Mr. Louda walked from the town up to the mountain hut. They passed each other at 10 AM. Mr. Rychlý hurried and reached his destination at 12 PM, while Mr. Louda moved slowly and reached the hut at 6 PM. At what time did they start their hike, given that each traveled at a constant speed?

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