
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 unit transplanted two types of large trees, type A and type B, with 2 trees each. The survival rates of type A and type B trees after transplantation are $\frac{2}{3}$ and $\frac{1}{2}$, respectively, and the survival of each tree is independent of others. The probability that exactly one tree of each type survives among the four transplanted trees is ______.

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