
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 side \(BC\) and on the extension of side \(AB\) through vertex \(B\) of triangle \(ABC\), points \(M\) and \(K\) are located, respectively, such that \(BM: MC = 4: 5\) and \(BK: AB = 1: 5\). Line \(KM\) intersects side \(AC\) at point \(N\). Find the ratio \(CN: AN\).

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