
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 each day from Monday to Friday. Vitya knows that with a probability of \( \frac{1}{2} \), the teacher will not check his homework during the school week, and with a probability of \( \frac{1}{2} \), the teacher will check it, but only once out of the five lessons, with equal chances on any day.

At the end of the math lesson on Thursday, Vitya realized that the teacher has not checked his homework yet 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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