
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  $ABCD$  be a rectangle with sides  $AB,BC,CD$  and  $DA$ . Let  $K,L$  be the midpoints of the sides  $BC,DA$  respectivily. The perpendicular from  $B$  to  $AK$  hits  $CL$  at  $M$ . Find  $$ \frac{[ABKM]}{[ABCL]} $$  

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