
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
Vitya has five math lessons per week, one on each day from Monday to Friday. He knows that there is a probability of \( \frac{1}{2} \) that the teacher will not check his homework at all during the week, and a probability of \( \frac{1}{2} \) that the teacher will check it, but only on one of the math lessons, with equal chances on any lesson.

At the end of his math lesson on Thursday, Vitya realized that the teacher has not yet checked his homework this week. What is the probability that the homework will be checked on Friday?

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