
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 subway during the first hour of the afternoon. Kolya arrives at the meeting place between noon and 1 PM, waits for 10 minutes, and leaves. Zhenya does the same.

a) What is the probability that they will meet?

b) How does the probability of meeting change if Zhenya decides to arrive earlier than 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 any random time between 12:00 PM and 12:50 PM, while Kolya still arrives between 12:00 PM and 1:00 PM?

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