
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 circle circumscribed around triangle \(FDC\), a tangent \(FK\) is drawn such that \(\angle KFC = 58^\circ\). Points \(K\) and \(D\) lie on opposite sides of line \(FC\) as shown in the diagram. Find the acute angle between the angle bisectors of \(\angle CFD\) and \(\angle FCD\). Provide your answer in degrees.

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