
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 triangle \(ABC\) with an area of 6, point \(K\) is taken on side \(AB\), dividing it in the ratio \(AK : BK = 2 : 3\), and point \(L\) is taken on side \(AC\), dividing \(AC\) in the ratio \(AL : LC = 5 : 3\). Point \(Q\) is the intersection of lines \(CK\) and \(BL\) and is at a distance of 1.5 from line \(AB\). Find the length of side \(AB\).

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