
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
Given triangle  $ABC$ , let  $D$  be an inner point of the side  $BC$ . Let  $P$  and  $Q$  be distinct inner points of the segment  $AD$ . Let  $K=BP\cap AC$ ,  $L=CP\cap AB$ ,  $E=BQ\cap AC$ ,  $F=CQ\cap AB$ .
Given that  $KL\parallel EF$ , find all possible values of the ratio  $BD:DC$ .

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