
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
One morning at 9:00 AM, a pedestrian named Fedya left the village of Fedino and headed towards the village of Novoverandovo. At the same time, a cyclist named Vera left Novoverandovo heading towards Fedya. It is known that by the time they met, Fedya had covered one-third of the distance between the villages. However, if Fedya had left an hour earlier, he would have covered half the distance by the time they met. At what time did Fedya and Vera meet? Assume that the speeds of Vera and Fedya are constant.

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