
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
[asy]
import olympiad;
import cse5;

size(5cm);

pointpen = black;
pair A = Drawing((10,17.32));
pair B = Drawing((0,0));
pair C = Drawing((20,0));

draw(A--B--C--cycle);

pair X = 0.85*A + 0.15*B;
pair Y = 0.82*A + 0.18*C;
pair W = (-11,0) + X;
pair Z = (19, 9);

draw(W--X, EndArrow);
draw(X--Y, EndArrow);
draw(Y--Z, EndArrow);

anglepen=black; anglefontpen=black;
MarkAngle("\theta", C,Y,Z, 3);
[/asy]

The cross-section of a prism with index of refraction  $1.5$  is an equilateral triangle, as shown above. A ray of light comes in horizontally from air into the prism, and has the opportunity to leave the prism, at an angle  $\theta$  with respect to the surface of the triangle. Find  $\theta$  in degrees and round to the nearest whole number. 

*(Ahaan Rungta, 5 points)*

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