
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

On Monday, Misha has five classes, and on Tuesday, he has six. To determine in which of these classes unpredictable teachers will ask him for his homework, Misha flips a coin 11 times – once for each possible occasion of being asked. If heads, Misha believes he will be asked about his homework in that class; if tails, he won't be asked. After his classes on Tuesday, Misha noted that he guessed correctly 7 times. Find the probability that exactly 3 of his correct predictions were for Monday.

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