
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 unit square.  $E$  and  $F$  trisect  $AB$  such that  $AE<AF. G$  and  $H$  trisect  $BC$  such that  $BG<BH. I$  and  $J$  bisect  $CD$  and  $DA,$  respectively. Let  $HJ$  and  $EI$  meet at  $K,$  and let  $GJ$  and  $FI$  meet at  $L.$  Compute the length  $KL.$ 

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