
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
Two tangents are drawn from an exterior point $A$ to a circle, touching the circle at points $B$ and $C$, respectively. A third tangent intersects segment $AB$ at $P$ and segment $AC$ at $R$, and touches the circle at $Q$. If $AB=24$, and $P$ divides $AB$ in a 3:1 ratio while $R$ divides $AC$ in a 1:3 ratio, find the perimeter of $\triangle APR$.
A) 40
B) 42
C) 48
D) 45
E) 50

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