
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
In a batch of \( N \) items, there are \( M \) marked items (\( M \leq N \)). A random selection of \( n \) items (\( n \leq N \)) is made from this batch. Find the probability that among these \( n \) items, there are exactly \( m \) (\( m \leq n \), \( m \leq M \)) marked items (event \( A \)).

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