
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
Given two basketball players, A and B, who take turns shooting until one of them makes a basket, the probability of A making a shot is 0.4, and the probability of B making a shot is 0.6. Let $\xi$ denote the number of shots A takes. If player A shoots first, calculate $P(\xi=k)$.

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