
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 isosceles  $\triangle ABC$  with  $AB = AC$  and  $\angle BAC = 22^{\circ}$ . On the side  $BC$  point  $D$  is chosen such that  $BD = 2CD$ . The foots of perpendiculars from  $B$  to lines  $AD$  and  $AC$  are points  $E$ ,  $F$  respectively. Find with the proof value of the angle  $\angle CEF$ .

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