
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 for each seed of a certain plant to germinate successfully is $\frac {1}{3}$, a plant research institute conducts a germination experiment with one dose of seeds per experiment, with the results of each experiment being independent. An experiment is considered successful if the seeds germinate; if not, it is considered a failure. If the institute conducts four experiments, let $\xi$ be the absolute value of the difference between the number of successful and failed experiments;  
(1) Calculate the expected value of the random variable $\xi$  
(2) Let event A denote "The solution set for the inequality $\xi x^2 - \xi x + 1 > 0$ is the set of all real numbers $\mathbb{R}$." Calculate the probability $P(A)$ of event A occurring.

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