
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 rhombus-shaped trivet has sides of $20 \mathrm{~cm}$ and a longer diagonal of $32 \mathrm{~cm}$. When slightly compressed along the longer diagonal, the other diagonal becomes longer by 1.2 times the amount of compression. What are the lengths of the diagonals after compression?

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