
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
In triangle $PQR$, where $PQ$ is the hypotenuse of the right triangle, a line segment starts moving from vertex $P$ to vertex $R$. The segment starts with zero length at $P$, continuously increases in length until it reaches a specific position, and then decreases back to zero length as it reaches $R$. Where does the segment attain its maximum length, and what is that length if $PQ = 10$ units and $PR = 6$ units?
A) 8 units
B) 10 units
C) $\sqrt{91}$ units
D) 6 units

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