
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 uniform solid semi-circular disk of radius  $R$  and negligible thickness rests on its diameter as shown. It is then tipped over by some angle  $\gamma$  with respect to the table. At what minimum angle  $\gamma$  will the disk lose balance and tumble over? Express your answer in degrees, rounded to the nearest integer. 

[asy]
draw(arc((2,0), 1, 0,180));
draw((0,0)--(4,0));
draw((0,-2.5)--(4,-2.5));
draw(arc((3-sqrt(2)/2, -4+sqrt(2)/2+1.5), 1, -45, 135));
draw((3-sqrt(2), -4+sqrt(2)+1.5)--(3, -4+1.5));
draw(anglemark((3-sqrt(2), -4+sqrt(2)+1.5), (3, -4+1.5), (0, -4+1.5)));
label(" $\gamma$ ", (2.8, -3.9+1.5), WNW, fontsize(8));
[/asy]

*Problem proposed by Ahaan Rungta*

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