
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
In the acute-angled triangle \(ABC\), the angle bisector \(AL\) and the median \(CM\) are drawn. Points \(K\) and \(N\) are the orthogonal projections of points \(L\) and \(M\) respectively onto the side \(AC\), with \(AK:KC = 4:1\) and \(AN:NC = 3:7\). Find the ratio \(AL\).

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