
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 each seed of a certain plant brought back from a spaceship successfully germinating is $\frac{1}{3}$, a botanical research institute conducts a germination experiment with these seeds. In each trial, a single seed is planted, and the outcomes of the trials are independent from each other. A trial is considered successful if the seed germinates, and a failure if it does not. If the research institute conducts four trials in total, let $\xi$ denote the absolute value of the difference between the number of successful trials and the number of failed trials by the end of the four trials.
(1) Find the probability that $\xi=2$.
(2) Find the probability that $\xi\geq 2$.

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