
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 side \(AB\) of triangle \(ABC\), points \(M\) and \(N\) are taken such that \(AM : MN : NB = 2 : 2 : 1\). On the side \(AC\), a point \(K\) is taken such that \(AK : KC = 1 : 2\). Find the area of the triangle \(MNK\) if the area of triangle \(ABC\) is 1.

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