
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
The midpoints of the sides of quadrilateral $ABCD$ are $K, L, M, N$ respectively. The midpoints of the sides of quadrilateral $KLMN$ are $P, Q, R, S$ respectively. For which quadrilaterals $ABCD$ will quadrilaterals $KLMN$ and $PQRS$ be similar?

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