
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
**Q8.** Given a triangle  $ABC$  and  $2$  point  $K \in AB, \; N \in BC$  such that  $BK=2AK, \; CN=2BN$  and  $Q$  is the common point of  $AN$  and  $CK$ . Compute  $\dfrac{ S_{ \triangle ABC}}{S_{\triangle BCQ}}.$ 

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