
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
Divide 52 volunteers into two groups, A and B, to participate in a voluntary tree-planting activity. Group A will plant 150 bundles of poplar saplings, and Group B will plant 200 bundles of sea buckthorn saplings. Assume that both groups start planting at the same time.

(1) According to statistics from previous years, it takes each volunteer $\dfrac{2}{5}$ hours to plant a bundle of poplar saplings and $\dfrac{1}{2}$ hours to plant a bundle of sea buckthorn saplings. How should the number of people in groups A and B be allocated so that the duration of the tree planting activity is minimized?

(2) After planting for one hour according to the allocation in (1), it is found that each volunteer still takes $\dfrac{2}{5}$ hours to plant a bundle of poplar saplings, but actually takes $\dfrac{2}{3}$ hours to plant a bundle of sea buckthorn saplings. Therefore, 6 volunteers are transferred from Group A to Group B to continue planting. Find the duration of the tree planting activity.

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