
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
Andrew has  $10$  balls in a bag, each a different color. He randomly picks a ball from the bag  $4$  times, with replacement. The expected number of distinct colors among the balls he picks is  $\tfrac{p}{q}$ , where  $\gcd(p, q) = 1$  and  $p, q > 0$ . What is  $p + q$ ?


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