
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
On the sides \( AB \) and \( AC \) of triangle \( ABC \), with area \( 36 \, \text{cm}^2 \), points \( M \) and \( K \) are taken respectively such that \( AM / MB = 1 / 3 \) and \( AK / KC = 2 / 1 \). Find the area of triangle \( AMK \).

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