
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 certain school in Wuhan uniformly uses a type of fluorescent tube from "Opple Lighting". It is known that the lifespan of this type of tube, denoted as $\xi$ (unit: months), follows a normal distribution $N\left( \mu ,\sigma ^{2} \right)$, and the probability that its lifespan is not less than 12 months is 0.8, and the probability that its lifespan is not less than 24 months is 0.2. Find:

(1) The average lifespan $\mu$ of this type of tube;  
(2) Assuming a classroom replaces 4 of these new tubes at once, and conducts an inspection after 12 months to replace any that have failed (no replacements in the meantime), find the probability that at least two tubes need to be replaced.

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