
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
Given a triangle \(ABC\) with \(AB=4\), \(BC=4\), and \(AC=1\). From point \(A\), an angle bisector is drawn that intersects the circumcircle of this triangle at point \(D\). Find the length \(DI\), where \(I\) is the incenter of triangle \(ABC\).

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