
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 $\triangle PQR$, the side $\overline{PQ}$ has a length of $12$. The bisector of angle $P$ meets $\overline{QR}$ at point $S$, where $QS = 4$. Calculate the possible range of values for the length of $PR$ and find the sum of the endpoints of this range.
A) 19
B) 20
C) 21
D) 22
E) 23

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