
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
While the Crakehams were refueling their car in a picturesque village, 8 children on their way to school stopped to watch them. The children had 32 apples in a basket that they planned to sell. Aunt Gertrude kindly bought all the apples and said the children could divide them among themselves.

Dora asked each child their name, and later that evening she said (though she made it a bit complicated): "Ann got 1 apple, Mary 2, Jane 3, and Kate 4. Ned Smith got as many apples as his sister. Tom Brown got twice as many apples as his sister, Bill Jones got three times as many apples as his sister, and Jack Robinson got four times as many apples as his sister."

Who can name the last names of each girl?

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