
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 is a parallelogram  $ABCD$ , with  $AB <AC <BC$ . Points  $E$  and  $F$  are selected on the circumcircle   $\omega$  of  $ABC$  so that the tangenst to  $\omega$  at these points pass through point  $D$  and the segments  $AD$  and  $CE$  intersect. 
It turned out that  $\angle ABF = \angle DCE$ . Find the angle  $\angle{ABC}$ .
A. Yakubov, S. Berlov

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