
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
Let  $K$ ,  $L$ ,  $M$ ,  $N$  be the midpoints of sides  $BC$ ,  $CD$ ,  $DA$ ,  $AB$  respectively of a convex quadrilateral  $ABCD$ . The common points of segments  $AK$ ,  $BL$ ,  $CM$ ,  $DN$  divide each of them into three parts. It is known that the ratio of the length of the medial part to the length of the whole segment is the same for all segments. Does this yield that  $ABCD$  is a parallelogram?

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