
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
From point \( A \), which is 5 units away from the center of a circle with a radius of 3 units, two secants \( A K C \) and \( A L B \) are drawn. The angle between them is \( 30^{\circ} \) (where \( K, C, L, B \) are the points of intersection of the secants with the circle). Find the area of triangle \( A K L \) if the area of triangle \( A B C \) is 10.

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