
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
An isosceles triangle $ABC$ with base $AB$ has vertex $C$ such that the altitude from $C$ to $AB$ measures $4$. A circle, rolling along side $AB$, has a radius of $2$. The circle remains tangent to $AB$ at a variable point $T$ and intersects lines $AC$ and $BC$ at points $M$ and $N$, respectively. Determine the number of degrees in arc $MTN$ for all possible positions of the circle.
A) $30^\circ$
B) $60^\circ$
C) $90^\circ$
D) $120^\circ$
E) $150^\circ$

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