
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 right triangle, $\triangle ABC$, with $\angle C = 90^\circ$, has an incircle that touches the hypotenuse and the other two sides at points $D$, $E$, and $F$ respectively. Calculate the nature of the angles in the triangle formed by connecting these points of tangency.
A) One right angle and two unequal acute angles
B) One obtuse angle, one acute angle (equals $45^\circ$), and one right angle
C) One obtuse angle, one right angle, and a $45^\circ$ angle
D) All angles are acute, two of which are equal
E) All unequal acute angles

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