
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 conference room is illuminated by 3 lamps, each using one energy-saving bulb of the same model. Assuming whether each lamp can illuminate normally only depends on the lifespan of the bulb, the probability that the lifespan of this model of bulb exceeds 1 year is 0.8, and the probability that the lifespan exceeds 2 years is 0.3. Bulb replacement is carried out annually, only replacing those that have failed, without replacing any that are still working.  
(I) During the first bulb replacement, calculate the probability of not needing to replace any bulbs and the probability of needing to replace 2 bulbs;  
(II) During the second bulb replacement, for one of the lamps, calculate the probability that the bulb needs to be replaced.

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