
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
Given a triangle \(ABC\) with an area of 1. Points \(P\), \(Q\), and \(R\) are taken on the medians \(AK\), \(BL\), and \(CN\) respectively such that \(AP = PK\), \(BQ : QL = 1 : 2\), and \(CR : RN = 5 : 4\). Find the area of triangle \(PQR\).

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