
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 uniform tetrahedron has its four faces numbered with 1, 2, 3, and 4. It is randomly thrown twice, and the numbers on the bottom face of the tetrahedron are $x_1$ and $x_2$, respectively. Let $t = (x_{1}-3)^{2}+(x_{2}-3)^{2}$.  
(1) Calculate the probabilities of $t$ reaching its maximum and minimum values, respectively;  
(2) Calculate the probability of $t \geq 4$.

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