
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
Points M and N are the midpoints of sides PC and PD of triangle PCD. As P moves along a line that is parallel to side CD, determine the number of the four quantities listed that change: the length of the segment MN, the perimeter of triangle PCD, the area of triangle PCD, the area of trapezoid CDNM.

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