
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 regular tetrahedron has its four faces marked with the numbers $1$, $2$, $3$, $4$. It is rolled randomly twice, and the numbers on the bottom face in the two rolls are $x_1$ and $x_2$ respectively. Let $t=(x_1-3)^2+(x_2-3)^2$.

1. Find the probabilities when $t$ takes its maximum and minimum values.
2. Find the probability that $t\geq 4$.

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