
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
The Chinese customs regulations stipulate that each batch of a certain type of product must undergo five consecutive inspections before export. If two indicators are found to be non-compliant, the batch cannot be exported, and the remaining inspections will not be conducted. It is known that the probability of failing any given inspection is 0.2. A batch of products is now being inspected for export.  
(1) Calculate the probability that this batch of products cannot be exported;  
(2) Calculate the probability that all five inspections must be completed to determine whether the batch of products can be exported. (Round to two decimal places) Reference data: $0.8^3=0.512$, $0.8^4=0.4096$, $0.8^5=0.32768$.

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