
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
Kolya and Zhenya agreed to meet in the metro sometime between noon and 1 PM. Kolya arrives at the meeting place at some random time between noon and 1 PM, waits for 10 minutes, and then leaves. Zhenya does the same.

a) What is the probability that they meet?

b) How does the probability of meeting change if Zhenya decides to arrive before 12:30 PM, while Kolya still arrives between noon and 1 PM?

c) How does the probability of meeting change if Zhenya decides to arrive at a random time between 12:00 and 12:50, while Kolya still arrives between 12:00 and 1:00?

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