
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 a right-angled triangle  $ABC$  ( $\angle A = 90^o$ ), the perpendicular bisector of  $BC$  intersects the line  $AC$  in  $K$  and the perpendicular bisector of  $BK$  intersects the line  $AB$  in  $L$ . If the line  $CL$  be the internal bisector of angle  $C$ , find all possible values for angles  $B$  and  $C$ .

by Mahdi Etesami Fard

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