
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
In square  $ABCD,$  points  $E$  and  $F$  are chosen in the interior of sides  $BC$  and  $CD$ , respectively. The line drawn from  $F$  perpendicular to  $AE$  passes through the intersection point  $G$  of  $AE$  and diagonal  $BD$ . A point  $K$  is chosen on  $FG$  such that  $|AK|= |EF|$ . Find  $\angle EKF.$ 

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