
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 rectangle $ABCD$, draw its diagonals and draw the angle bisector originating from vertex $C$. The angle bisector intersects side $AB$ at point $E$, diagonal $BD$ at point $F$, and the intersection of the diagonals is point $O$.

What angle does the angle bisector make with the $AC$ diagonal, given that triangles $EOB$ and $EOF$ are isosceles?

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