
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 the diagram below, we have \(\sin \angle APB = \frac{3}{5}\). What is \(\sin \angle APC\)?

[asy]
pair A,P,B,C;
C = (-2,0);
P = (0,0);
B = (2,0);
A = rotate(aSin(3/5))*(1.5,0);
dot("$C$",C,S);
dot("$B$",B,S);
dot("$A$",A,N);
dot("$P$",P,S);
draw(B--C);
draw(P--A);
[/asy]

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