
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 $A$ and $B$ move along two lines, both parallel to a fixed line segment $PQ$, with $P$ being the midpoint of $AB$. How many of the four quantities change: the length of the segment $AB$, the perimeter of $\triangle APB$, the area of $\triangle APB$, the distance between midpoint $P$ and line $AB$?

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