
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
Two basketball players, A and B, take turns shooting hoops until someone makes a shot. The probability of A making a shot each time is $0.4$, and the probability of B making a shot is $0.6$. These probabilities are not affected by the results of other shots. Let $X$ represent the number of times A shoots. If A shoots first, calculate the probability that $X=k$.

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