
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 a right isosceles triangle $ABC$ with $AC=BC$ and right angle at $C$. A circle with radius equal to the altitude of triangle $ABC$ rolls along the leg $AC$, remaining tangent to it at a variable point $T$ and intersecting the hypotenuse $AB$ and the leg $BC$ at points $M$ and $N$, respectively. Let $n$ be the number of degrees in arc $MTN$. Determine how $n$ varies for all permissible positions of the circle.
A) Varies from $0^\circ$ to $180^\circ$
B) Varies from $30^\circ$ to $60^\circ$
C) Varies from $0^\circ$ to $90^\circ$
D) Varies from $45^\circ$ to $90^\circ$
E) Remains constant at $90^\circ$

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