
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
Let  $AK$  and  $AT$  be the bisector and the median of an acute-angled triangle  $ABC$  with  $AC > AB$ . The line  $AT$  meets the circumcircle of  $ABC$  at point  $D$ . Point  $F$  is the reflection of  $K$  about  $T$ . If the angles of  $ABC$  are known, find the value of angle  $FDA$ .

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