
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
In a dance hall, there are 15 boys and 15 girls arranged in two parallel rows such that 15 dance pairs are formed. It so happens that the height difference between the boy and the girl in each pair does not exceed $10 \mathrm{~cm}$. Demonstrate that if we place the same boys and girls in two parallel rows in ascending order of heights, the height difference between the members of the newly formed pairs will also not exceed $10 \mathrm{~cm}$.

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