
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 parallelogram \(ABCD\) where \(AB < AC < BC\). Points \(E\) and \(F\) are chosen on the circumcircle \(\omega\) of triangle \(ABC\) such that the tangents to \(\omega\) at these points pass through point \(D\); moreover, segments \(AD\) and \(CE\) intersect. It is found that \(\angle ABF = \angle DCE\). Find the angle \(ABC\).

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