
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 $\triangle PCD$, where $C$ and $D$ have fixed positions and point $P$ moves along a line parallel to line $CD$. Determine the number of the four given quantities that change as $P$ is moved.

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