
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
Shooting is conducted at a certain target until the first hit with no limit on the number of shots. Find the expected value and the variance of the number of shots fired if the probability of hitting the target with each shot is the same and equal to $p$.

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