
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 $PQR$, the lengths are $PQ = 13$, $QR = 20$, and $RP = 15$. The angle bisector of $\angle PQR$ intersects $QR$ at point $S$ and the circumcircle of $\triangle PQR$ at point $T \ne P$. The circumcircle of $\triangle PST$ intersects line $PQ$ at points $P$ and $U \ne P$. Find the length of $RU$.
A) 18
B) 19
C) 20
D) 21
E) 22

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