
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
Triangle $PQR$ is inscribed in circle $\Omega$ with $PQ=6$, $QR=8$, $PR=4$. The bisector of angle $P$ meets side $\overline{QR}$ at $S$ and circle $\Omega$ at a second point $T$. Let $\delta$ be the circle with diameter $\overline{ST}$. Circles $\Omega$ and $\delta$ meet at $T$ and a second point $U$. Find $PU^2$.

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