
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 $\triangle ABC$, assume a point $L$ lies on side $AC$ such that $AL = 6$. The point $K$ lies on side $BC$, such that $AK$ is an altitude of $\triangle ABC$ and $BK = 9$. If $BC = 15$ and $AC = 12$, find the area of $\triangle ABC$.

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