
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
At nine o'clock in the morning, Paul set off on his bicycle from point $A$ to point $B$ at a speed of 15 km/h. At a quarter to ten, Peter set off from $B$ to $A$ at a speed of 20 km/h. They agreed to have a picnic halfway and fulfilled this condition exactly. At what time did they meet?

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