
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
A quadrilateral $ABCD$ is inscribed in a circle. A smaller circle is inscribed inside the quadrilateral that touches all four sides. From a point $P$ outside both circles, tangents $PA$, $PB$, $PC$, and $PD$ to the larger circle, and $PT$, $PU$, $PV$, and $PW$ to the smaller circle are drawn. Find the sum of the angles formed between the tangents to the larger circle and the tangents to the smaller circle.
A) 180°
B) 360°
C) 540°
D) 720°
E) 1080°

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