
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 person is shooting, and the probability of hitting the target each time is 0.8. It is stipulated that if the target is hit, the shooting will stop; if the target is missed, the shooting will continue. If there are only 3 bullets, the expected number of shots $\xi$ is (answer with a number).

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