
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
Consider an isosceles triangle $DEF$ with $DE = EF$ and a base $DF$. The altitude from $E$ to $DF$, which equals the length of $DF$, is twice the radius of a circle. The circle rolls along $DF$, staying tangent at variable point $P$ and intersecting lines $DE$ and $EF$ in points $R$ and $S$, respectively. Determine the number of degrees in arc $RS$ as the circle achieves all permissible positions along $DF$:
A) varies from $45^\circ$ to $90^\circ$  
B) varies from $45^\circ$ to $135^\circ$  
C) remains constant at $90^\circ$  
D) remains constant at $45^\circ$  
E) varies from $90^\circ$ to $180^\circ$
A) $45^\circ$ to $90^\circ$  
B) $45^\circ$ to $135^\circ$  
C) Constant at $90^\circ$  
D) Constant at $45^\circ$  
E) $90^\circ$ to $180^\circ$

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