
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
A bag contains $7$ balls that are identical in all aspects except for color, with $5$ red balls and $2$ black balls. Balls are randomly drawn from the bag one by one without replacement until $3$ balls have been drawn. Let $\xi$ represent the number of black balls drawn. Calculate the expected value $E(\xi)$, and express your answer as a simplified fraction.

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