
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
Given that the probability of a certain type of animal having a particular disease is 0.1, blood tests are used to determine whether the animal has the disease. If the test result is positive, the animal has the disease, and if it is negative, the animal does not have the disease. When testing multiple animals, their blood samples can be tested individually or mixed together. If at least one animal's blood in the mixed sample tests positive, the mixed sample will also test positive, requiring individual tests for that group.

1. Find the probability that a mixed blood sample from 2 of these animals will test positive.
2. Now, there are blood samples from 4 of these animals that need to be tested. There are three plans:
   Plan 1: Test each sample individually.
   Plan 2: Divide the samples evenly into two groups for testing.
   Plan 3: Mix all the samples together and test them as one.

Which plan is more suitable (i.e., has the smallest expected number of tests)?

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