
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
Given that segment AB = 16, and segment BC = 10 is cut on line AB, points P and Q are the midpoints of AB and AC, respectively.
(1) Find the length of segment PQ.
(2) If AB = m and BC = n, with other conditions unchanged, find the length of segment PQ.
(3) Analyze the conclusions of (1) and (2) and discuss any patterns discovered.

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