
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
Segment \(AB\) has midpoint \(C\), and segment \(BC\) has midpoint \(D\). Semi-circles are constructed with diameters \(\overline{AB}\) and \(\overline{BC}\) to form the entire region shown. Segment \(CP\) splits the region into parts with area ratio \(2:3\). If \(CP\) starts from \(C\) and terminates at the perimeter of the semicircle on \(\overline{AB}\), what is the degree measure of angle \(ACP\)? Express your answer as a decimal to the nearest tenth.
 
[asy]
draw((0,0)--10dir(180),linewidth(2));
draw((0,0)--10dir(40),linewidth(2));  // Adjust the angle here to approximately show the 2:3 ratio visually
draw((0,0)--10dir(0),dashed);

draw(10dir(180)..10dir(90)..10dir(0),linewidth(2));

draw((5,0)+3.33dir(180)..(5,0)+3.33dir(-90)..(5,0)+3.33dir(0),linewidth(2));

dot((0,0));
dot((5,0));

label("A",10dir(180),W);
label("B",10dir(0),E);
label("C",(0,0),SW);
label("D",3.33dir(0),NE);
label("P",10dir(40),NE);
[/asy]

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